Publications and Manuscripts — A J van der Poorten[1]‘A note on the independence of the axioms for a vector space’, J. Austral. Math. Soc. 7 (1967),
425–428[2]‘Transcendental entire functions mapping every algebraic number field into itself’, J. Austral.
Math. Soc. 8 (1968), 192–193[3]‘On a sequence of prime numbers’ (with C. D. Cox), J. Austral. Math. Soc. 8 (1968), 571–574[4]‘Generalisations of Turán’s main theorems on lower bounds for sums of powers’, Bull. Austral.
Math. Soc.(1970), 15–37[5]‘A generalisation of Turán’s main theorems to binomials and logarithms’, Bull. Austral. Math.
Soc. 3 (1970), 183–195[6]‘On the arithmetic nature of definite integrals of rational functions’, Proc. Amer. Math. Soc.
29 (1971), 451–456[7]‘Perfect approximation of functions’, Bull. Austral. Math. Soc. 5 (1971), 117–126[8]‘On a theorem of Dancs and Turán’, Acta Math. Acad. Sci. Hungar. 22 (1971), 359–364[9]‘Generalising Turán’s main theorems’, Acta Math. Acad. Sci. Hungar. 24 (1973), 93–96[10]‘A note on recurrence sequences’, Proc. J. Roy. Soc. NSW 106 (1973), 115–117[11]‘Extremally disconnected topological groups’ (with S. A. Morris), Proc. J. Roy. Soc. NSW 107(1974), 114–115[12]‘Closed subgroups of products of reals’ (with D. C. Hunt and S. A. Morris), Bull. Lond. Math.
Soc. 7 (1975), 124–128[13]‘Some determinants that should be better known’, J. Austral. Math. Soc. 21 (1976), 278–288[14]‘Algebraic functions satisfying a class of functional equations’ (with J. H. Loxton), Aequationes
Math. 14 (1976), 413–420[15]‘Arithmetic properties of certain functions in several variables’ (with J. H. Loxton), J. Number
Theory 9 (1977), 87–106[16]‘A note on the simultaneous polynomial approximation of exponential functions’ (with J. H. Loxton), Bull. Austral. Math. Soc. 11 (1974), 333–338[17]‘On the number of zeros of certain functions’ (with M. Voorhoeve and R. Tijdeman), Proc.
Kon. Nederl. Akad. v. Wetenschappen Ser. A 78 (1975), 407–416 = Indag. Math. 37 (1975),
407–416[18]‘Zeros of p-adic exponential polynomials’, Proc. Kon. Nederl. Akad. v. Wetenschappen Ser. A
79 (1976), 46–49 = Indag. Math. 38 (1976), 46–49[19]‘Arithmetic implications of the distribution of integral zeros of exponential polynomials’, Séminaire
Delange--Pisot--Poitou (Théorie des nombres)(16e année: 1974/1975), Fasc.1, exp. n◦ 11, 9pp(Secrétariat Mathématique, Paris, 1975)[20]‘Propriétes arithmétiques et algébriques de fonctions satisfaisant une classe d’équations fonctionelles’, Séminaire de théorie des nombres (Université de Bordeaux I)(1974–1975), exp. n◦ 7 ,13pp. (lab. de théorie des nombres, CNRS, Talence, 1975)[21]‘Zéros communs de plusieurs polynômes exponentielles’, Séminaire de théorie des nombres (Université de Bordeaux I)(1974–1975), exp. n◦ 8 , 6pp. (lab. de théorie des nombres, CNRS, Talence,
1975)

[22]

‘A class of hypertranscendental functions’ (with J. H. Loxton), Aequationes Math. 16 (1977),
93–106

2

A. J. van der Poorten — Manuscripts and Publications — July, 2007[23]

‘On the distribution of zeros of exponential polynomials’, Math. Slovaca 26 (1976), 299–307[24]‘Multidimensional generalisations of the Padé table’ (with J. H. Loxton), Rocky Mountains J.
of Math. 9 (1979), 385–393[25]‘On common zeros of exponential polynomials’ (with R. Tijdeman), L’Enseignement Math. IIesérie 21 (1975), 57–67[26]‘A note on the zeros of exponential polynomials’, Compositio Math. 31 (1975), 109–113[27]‘Wronskian determinants and the zeros of certain functions’ (with M. Voorhoeve), Proc. Kon.
Nederl. Akad. v. Wetenschappen Ser. A 78 (1975), 417–424 = Indag. Math. 37 (1976), 417–424[28]‘Hermite interpolation and p-adic exponential polynomials’, (to George Szekeres on his 65thbirthday) J. Austral. Math. Soc. (Series A) 22 (1976), 12–26[29]‘On Baker’s inequality for linear forms in the logarithms of algebraic numbers’, Math. Proc.
Camb. Phil. Soc. 80 (1976), 233–248[30]‘Effectively computable bounds for the solutions of certain diophantine equations’, Acta Arith.
XXXIII (1977), 193–207[31]‘Arithmetic properties of certain functions in several variables II’ (with J. H. Loxton), J. Austral.
Math. Soc. (Series A) 24 (1977), 393–408[32]‘On the transcendence and algebraic independence of certain somewhat amusing numbers’,Séminaire de théorie des nombres (Université de Bordeaux I)(1975–1976), exp. n◦ 14 , 13pp
(lab. de théorie des nombres, CNRS, Talence, 1976)[33]‘Computing the lower bound for linear forms in logarithms’, Séminaire Delange--Pisot-Poitou(Théorie des nombres)(17e année: 1975/1976), Fasc.1, exp. n◦ 17, 9pp (Secrétariat Mathématique, Paris, 1976)[34]‘Arithmetic properties of certain functions in several variables III’ (with J. H. Loxton), Bull.
Austral. Math. Soc. 16 (1977), 15–47.

[35]‘Computing the effectively computable bound in Baker’s inequality for linear forms in logarithms’ (with J. H. Loxton), Bull. Austral. Math. Soc. 15 (1976), 36–57[36]‘Transcendence and algebraic independence by a method of Mahler’ (with J. H. Loxton), in
Transcendence theory — advances and applications, ed. A. Baker and D. W. Masser, (Academic
Press London and New York, 1977), Chapter 15, 211–226[37]‘Linear forms in logarithms in the p-adic case’, in Transcendence theory — advances and applications, ed. A. Baker and D. W. Masser, (Academic Press London and New York, 1977),
Chapter 2, 29– 57[38]‘On the number of zeros of functions’, L’Enseignement Math. IIe série 23 (1977), 19–38[39]‘Applications of the Gel’fond–Baker method to diophantine equations’ (with A. Schinzel, T. N.
Shorey and R. Tijdeman), in Transcendence theory — advances and applications, ed. A. Baker
and D. W. Masser, (Academic Press London and New York, 1977), Chapter 3, 59–77[40]‘Multiplicative relations in number fields’ (with J. H. Loxton), Bull. Austral. Math. Soc. 16(1977), 83–98[40c]‘Computing the effectively computable bound in Baker’s inequality for linear forms in logarithms’, and ‘Multiplicative relations in number fields’ (with J. H. Loxton), : Corrigenda andaddenda Bull. Austral. Math. Soc. 17 (1977), 151–155[41]‘On the growth of recurrence sequences’ (with Loxton, J. H.), Math. Proc. Camb. Phil. Soc. 81(1977), 369-376[42]‘Some remarks on Fermat’s conjecture’ (with K. Inkeri), Acta Arith. XXXVI (1980), 107–111[43]‘The polynomial X 3 + X 2 + X − 1 and elliptic curves of conductor 11’, Séminaire DelangePisot-Poitou (Théorie des nombres) (18e année: 1976/1977), Fasc.1, exp. n◦ 17, 7pp (Secrétariat
Mathématique, Paris, 1977)

A. J. van der Poorten — Manuscripts and Publications — July, 2007

[44]

‘Algebraic independence properties of the Fredholm series’ (with J. H. Loxton), (to Kurt Mahler
on his 75th birthday) J. Austral. Math. Soc. (Series A) 26 (1978), 31–45[45]‘A proof that Euler missed . . . Apéry’s proof of the irrationality of ζ(3) ; An informal report’,
The Mathematical Intelligencer 1 (1979), 195-203[46]‘Elliptic curves of conductor 11’ (with M. K. Agrawal, J. H. Coates and D. C. Hunt), Math.
Comp. 34 (1980), 991–1002[47]‘Some wonderful formulae . . . footnotes to Apéry’s proof of the irrationality of ζ(3)’, Séminaire
Delange--Pisot-Poitou (Théorie des nombres) (20e année: 1978/1979), Fasc.2, exp. n◦ 29, 7pp(Secrétariat Mathématique, Paris, 1980)[48]‘Some wonderful formulas . . . an introduction to polylogarithms’, Queen’s Papers in Pure andApplied Mathematics 54 (1980), 269–286[49]‘On strong pseudoprimes in arithmetic progression’ (with A. Rotkiewicz), J. Austral. Math.
Soc. (Series A) 29 (1980), 316–321[50]‘Arithmetic properties of the solutions of a class of functional equations’ (with J. H. Loxton),
J. für Math. (Crelle) 330 (1982), 159–172[50t]‘Euclidean number fields’(translation and revision with H. W. Lenstra Jr.), The MathematicalIntelligencer 2 (1980), 6–15; II: ibid 2 (1980), 73–77; III: ibid 2 (1980), 99–103[51]‘Linear forms in logarithms, effectivity and elliptic curves’, Mémoire Soc. Math. France 2e série
2 (1980), p71[52]‘Arithmetic and analytic properties of paperfolding sequences’ (with Mendès France, M.), Bull.
Austral. Math. Soc. 24 (1981), 123–131[53]‘Substitution automata, functional equations and functions algebraic over a finite field’, Contemporary Math. 9 (1982), 307–312[54]‘Bounds for solutions of systems of linear equations’ (with Jeffrey D. Vaaler), Bull. Austral.
Math. Soc. 25 (1982), 125–132[55]‘Multiplicative dependence in number fields’ (with J. H. Loxton), Acta Arith. LII (1983), 291–
302

[56]

‘Identifying a rational function’ (with J. P. Glass and J. H. Loxton), C. R. Math. Rep. Acad.
Sc. Canada 3 (1981), 279–284[56c]‘Identification of rational functions; lost and regained’, C. R. Math. Rep. Acad. Sc. Canada 4(1982), 309–314[57]‘Some problems of recurrent interest’, in Topics in Number Theory, (Coll. Math. Soc. János
Bolyai 34 Budapest 1981) (North Holland 1984), 1265–1294[57f]

Foreword to Leonard Lewin, Polylogarithms and associated functions, North-Holland PublishingCo., New York–Amsterdam, 1981, xvii+359 pp[58]‘FOLDS!’ (with Michel Dekking and Michel Mendès France), The Mathematical Intelligencer 4(1982), 130-138; II: ‘Symmetry disturbed’, ibid. 173-181; III: ‘More morphisms’, ibid. 190-195[59]‘The growth conditions for recurrence sequences’ (with H. P. Schlickewei), Macquarie Math.
Reports (Macquarie University, NSW 2109 Australia) 41 (1982), 27pp

[60]

‘Effective approximation of algebraic numbers (d’après Enrico Bombieri)’, Séminaire de théorie
des nombres (Université de Bordeaux I)(1982–1983), exp.8 , 13pp (lab. de théorie des nombres,
CNRS, Talence, 1983)[61]‘Hadamard operations on rational functions’, Groupe d’ étude d’ analyse ultramétrique (Amice,
Barsky, Robba)(10e année: 1982/1983), exp. n◦ 4, 11pp (Secrétariat Mathématique, Paris, 1983)[62]‘A dozen years is but a day’, Austral. Math. Soc. Gazette 11 (1984), 33–34

3

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A. J. van der Poorten — Manuscripts and Publications — July, 2007

[63]

‘Additive relations in number fields’, in Séminaire de théorie des nombres de Paris (Delange–
Pisot–Poitou) 1982–83, (Birkhäuser 1984), 259–266[64]‘Automata and p-adic numbers’ (with M. Mendès France), in Analytic and elementary number
theory, (Marseille, 1983) Publ. Math. Orsay 86–1, Univ. Paris XI, Orsay, 1986[65]

‘p-adic methods in the study of Taylor coefficients of rational functions’, (to Kurt Mahler on
his 80th birthday) Bull. Austral. Math. Soc. (Series A) 28 (1984), 109–117[65q] ‘The longest prime’, The Math. Intelligencer 7 (1985), p.40
[66]

‘Automata and the arithmetic of formal power series’ (with M. Mendès France), Acta Arith.
XLVI (1986), 211-214[67]‘Thue’s method and curves with prescribed singularities’, Macquarie Math. Reports (Macquarie
University, NSW 2109 Australia) 48 (1984), 14pp

[68]

‘Integers with digits 0 or 1’ (with D. H. Lehmer and K. Mahler), Math. Comp. 46 (1986),
683–689[69]‘An awful problem about integers in base 4’ (with J. H. Loxton), (to Paul Erdős on his 75thbirthday) Acta Arith. XLIX (1987), 193–203[70]‘Zeros of p-adic exponential polynomials II’ (with Robert S. Rumely), J. Lond. Math. Soc. 36(1987), 1–15

[71]

‘A note on the Hadamard k th root of a rational function’ (with Robert S. Rumely), J. Austral.
Math. Soc. (Series A) 43 (1987), 314–327[72]‘A bridge problem’, Austral. Math. Soc. Gazette 13 (1986), p92[73]‘A lower bound for linear forms in the logarithms of algebraic numbers’ (with J. H. Loxton, M.
Mignotte and M. Waldschmidt), C. R. Math. Rep. Acad. Sc. Canada 9 (1987), 119–124[74]‘Remarks on generalised power sums’ (with Robert S. Rumely), Bull. Austral. Math. Soc. 36(1987), 311–329[74a] ‘Remarks on the continued fractions of algebraic numbers’, Groupe de travail en théorie analytique et élémentaire des nombres, (1986–87), Publ. Math. Orsay 88, 89–90[75]‘An introduction to continued fractions’, in Diophantine Analysis, LMS Lecture Notes in Math.
109, ed. J. H. Loxton and A. J. van der Poorten, (Cambridge University Press 1986), 99–138[75e](edited, with J. H. Loxton), Diophantine Analysis, LMS Lecture Notes in Math. 109 (Cambridge University Press 1986), 170pp.

[76]‘Some quantitative results related to Roth’s theorem’ (with E. Bombieri), J. Austral. Math.
Soc. (Series A) 45 (1988), 233–248[77]‘Solution de la conjecture de Pisot sur le quotient de Hadamard de deux fractions rationnelles’,C. R. Acad. Sc. Paris (Série 1) 306 (1988), 97–102.

[77m] Robert Rumely, ‘Notes on van der Poorten’s proof of the Hadamard Quotient Theorem’, Sém. deThéorie des Nombres, Paris 1986–87, Catherine Goldstein ed., Progress in Math. 75, Birkhäuser
Boston Inc. 1989, 349–409.
[78]‘Remarks on automata, functional equations and transcendence’, Séminaire de théorie des nombres (Université de Bordeaux I)(1986–1987), exp. n◦ 27 , 11pp (lab. de théorie des nombres,
CNRS, Talence, 1987)[79]‘Indépendance algébrique de certaines séries formelles’ (with J.-P. Allouche and M. Mendès
France), Bull. Soc. Math. France 116 (1988), 449–454[80]‘From geometry to Euler identities’ (with M. Mendès France), Theoretical Computing Science
65 (1989), 213–220[81]‘Remarks on Roth’s theorem’, in Séminaire de théorie des nombres Paris 1986–87, (Birkhäuser
Boston, 1989), 443–452

A. J. van der Poorten — Manuscripts and Publications — July, 2007[82]

‘Integer-valued p-adic functions’ (with V. Laohakosol and J. H. Loxton), in Number theory, ed.
K. Győry and G. Halász (Coll. Math. Soc. János Bolyai 51 Budapest 1987) (North-Holland,1990), 829–849[83]‘Arithmetic properties of automata: regular sequences’ (with J. H. Loxton), J. für Math. 392(1988), 57–69[83o] ‘Kurt Mahler 1903-1988’, The Austral. Math. Soc. Gazette 15 (1988), 26–27[84]‘Rational functions, diagonals, automata and arithmetic’ (with Leonard Lipshitz), in Number
Theory, ed. Richard A. Mollin, (First Conference of the Canadian Number Theory Association,
Banff 1988) (Walter de Gruyter Berlin·New York, 1990), 339–358.

[85]‘Some facts that should be better known; especially about rational functions’, in Number Theory
and Applications, ed. Richard A. Mollin, (NATO – Advanced Study Institute, Banff, 1988)(Kluwer Academic Publishers Dordrecht, 1989), 497–528.

[86]‘Factorisation in the ring of exponential polynomials’ (with G. R. Everest), Proc. Amer. Math.
Soc. 125.5 (1997), 1293–1298[87]‘A full characterisation of divisibility sequences’ (with J.–P. Bézivin and A. Pethő), Amer. J.
Math. 112 (1990), 985–1001[88]‘On the thermodynamics of curves and other curlicues’ (with R. R. Moore), in Geometry andPhysics, ed. M. N. Barber and M. K. Murray, Proc. CMA 22 (Canberra, 1989), 82–109[89]‘A divergent argument concerning Hadamard roots of rational functions’, in Analytic number
theory, (Proceedings of a conference in honour of Paul T. Bateman, Allerton Park 1989) ed.
B. C. Berndt, H. G. Diamond, H. Halberstam and A. Hildebrand (Birkhäuser Boston, 1990),
413–427[90]‘Fractions of the period of the continued fraction expansion of quadratic integers’, Bull. Austral.
Math. Soc. 44 (1991), 155–169[91]‘Generalised simultaneous approximation of functions’ (dedicated to the memory of Kurt Mahler),
J. Austral. Math. Soc. , 51 (1991), 50–61[91c]‘Some quantitative results related to Roth’s theorem: Corrigenda’ (with E. Bombieri), J. Austral. Math. Soc. (Series A) 48 (1990), 154–155[92]‘Additive relations in fields’ (with H. P. Schlickewei), J. Austral. Math. Soc., 51 (1991), 154–170[92o] ‘Kurt Mahler’, (Brief obituary) The Australian Academy of Science Year Book (1990/91), 75–77[93]‘Dyson’s lemma without tears’ (with F. Beukers and R. I. Yager), Indag. Math. 2, (New Series)(1991), 1–8[94]‘Notes on continued fractions and recurrence sequences’, in Number theory and cryptography,
ed. J. H. Loxton, LMS Lecture Notes in Mathematics 154 (Cambridge University Press 1990),
Chapter 6, 86–97.

[95]‘A Diophantine problem in harmonic analysis’ (with H. P. Schlickewei), Math. Proc. Camb.
Phil. Soc. 108 (1990), 417–420.

[96]‘Some explicit continued fraction expansions’ (with M. Mendès France), Mathematika 38 (1991),
1–9.

[97]

‘An infinite product with bounded partial quotients’ (with J.–P. Allouche and M. Mendès
France), Acta Arith. 59 (1991), 171–182[98]‘Folded continued fractions’ (with J. Shallit), J. Number Theory 40 (1992), 237–250[99]‘Zeros of recurrence sequences’ (with H. P. Schlickewei), Bull. Austral. Math. Soc. 44 (1991),
215–223[99o] ‘Obituary: Kurt Mahler 1903–1988’, J. Austral. Math. Soc. 51 (1991), 343–380.
[100] ‘The Eisenstein constant’ (with B. M. Dwork), Duke Math. J. 65 (1992), 23–43.

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A. J. van der Poorten — Manuscripts and Publications — July, 2007

[100c] ‘Corrections to “The Eisenstein constant” ’ (with B. M. Dwork), Duke Math. J. 76 (1994),
669–672.
[101] ‘Schneider’s continued fraction’ in Number theory with emphasis on the Markoff spectrum,
William Moran and Andrew D. Pollington eds., (Marcel Dekker, 1993), 271–281.
[102] ‘A specialised continued fraction’ (with J. Shallit), Canad. J. Math. 45 (1993), 1067-1079.
[103] ‘Power series representing algebraic functions’, in Séminaire de théorie des nombres Paris 1990–
91 , S. David ed. (Birkhäuser Boston, 1992), 241–262.
[104] ‘On the number of zeros of exponential polynomials and related questions’ (with I. E. Shparlinski), Bull. Austral. Math. Soc. 46 (1992), 399–410.
[105] ‘A note on length and angle’ (with R. C. Talent), Nieuw Archief voor Wiskunde (4e serie) 11(1992), 19–25[106] ‘Some problems concerning recurrence sequences’ (with G. Myerson), Amer. Math. Monthly
102 (1995), 698–705.
[107] ‘Continued fractions of formal power series’ (dedicated to Paulo Ribenboim), in Advances in
Number Theory (Proceedings of the 3rd Conference of the CNTA, Kingston 1991) ed. Fernando
Q. Gouvêa and Noriko Yui (The Clarendon Press, Oxford 1993), 453–466.
[108] ‘A note on symmetry and ambiguity’ (with Richard A. Mollin), Bull. Austral. Math. Soc., 51(1995), 215–233.
[109] ‘Divisibility sequences, continued fractions, and the HQT,’ prepared for Proc. 23rd Annual Iranian Mathematics Conference (April, 1992 Bakhtaran, Iran) ed. S. M. Shahrtash = Macquarie
Number Theory Reports 92–109 (August 1992)[110] ‘Kurt Mahler 26 July 1903–26 February 1988’ (with J. H. Coates), Biographical Memoirs ofFellows of the Royal Society (The Royal Society London) 39 (1994), 265–279 and in Historical
Records of Australian Science, 9 (1993), 369–385[111] ‘Halfway to a solution of X 2 − DY 2 = −3’ (with R. A. Mollin and H. C. Williams), J. Théorie
de Nombres de Bordeaux , 6 (1994), 421–459.
[112] ‘Effective measures of irrationality for cubic extensions of number fields’ (with Enrico Bombieriand Jeffrey D. Vaaler), Annali della Scuola Normale di Pisa (Classe di scienze), 23 (1996),
211–248.
[113] ‘Continued fractions of algebraic numbers’ (with Enrico Bombieri), Computational Algebra andNumber Theory, Sydney 1992, Wieb Bosma and Alf van der Poorten eds., Kluwer 1995, 138–154.
[114] ‘Determinants in the study of Thue’s method and curves with prescribed singularities’ (with
E. Bombieri and D. C. Hunt), J. Experimental Math., 4 (1995), 101–110.
[115] ‘Composition of forms, ideals and continued fractions’, manuscript, currently of 5pp, in preparation for, say, Amer. Math. Monthly[115t] Preparation of English translation of Classical Diophantine Equations by V. G. Sprindžuk,
Springer Lecture Notes in Mathematics 1559 (1993) Springer-Verlag, 229 + x pp[116] ‘Some infinite products with interesting continued fraction expansions’ (with C. G. Pinner andSaradha Natarajan), J. Théorie des Nombres de Bordeaux , 5 (1993), 187–216[117] ‘Continued fraction expansions of values of the exponential function and related fun with continued fractions’, Nieuw Archiev v. Wiskunde, vierde serie, 14 (1996), 221–230[118] ‘Explicit quadratic reciprocity’, in Number Theoretic and Algebraic Methods in Computer Science, Moscow 1993 , Alf van der Poorten, Igor Shparlinski and Horst G. Zimmer eds., World
Scientific 1995, 175–180.
[119] Notes on Fermat’s Last Theorem, (New York, N. Y.: Wiley-Interscience, 1996), xvi+222pp.

A. J. van der Poorten — Manuscripts and Publications — July, 2007[120] ‘Explicit formulas for units in certain quadratic number fields’, in Algorithmic Number Theory(1st Algorithmic Number Theory Symposium — Cornell University, May 6–9, 1994), Lecture
Notes in Computer Science 887, Springer-Verlag 1994, 194–208[121] ‘On certain continued fraction expansions of fixed period length’ (with H. C. Williams), Acta
Arith. 89 (1999), 23–35.
[122] ‘On sequences of polynomials defined by certain recurrence relations’ (with I. E. Shparlinski),Acta Sci. Math. (Szeged) 61 (1995), 75–101[123] ‘On linear recurrence sequences with polynomial coefficients’ (with I. E. Shparlinski), Glasgow
Math. J., 38 (1996), 147–155[124] ‘Factorisation in fractional powers’, Acta Arith., LXX (1995), 287–293[125] ‘The Lech-Mahler theorem . . . with tears’, 6pp[126] ‘A note on Hadamard roots of rational functions’ (to Wolfgang Schmidt on the occasion of thecelebration of his 60th birthday), Rocky Mountains J. Math. 26 (1996), 1183–1197[127] ‘Concerning commuting’, Austral. Math. Soc. Gazette 21 (1994), p68[128] ‘Substitution invariant Beatty sequences’ (with Takao Komatsu), Japan J. Math. 22 (2; 8)(1996), 349–354[129] ‘Remarks on Fermat’s Last Theorem’, Austral. Math. Soc. Gazette 21 (1994), 150–159[129e] (edited, with Wieb Bosma) Computational Algebra and Number Theory, Sydney 1992 , Kluwer
1995, 321+ xii pp[130e] (edited, with Igor Shparlinski and Horst G. Zimmer) Number Theoretic and Algebraic Methods
in Computer Science, Moscow 1993 , World Scientific 1995, 205+ vii pp[131] ‘Convergents of folded continued fractions’, (with Jean-Paul Allouche, Anna Lubiw, Michel
Mendès France and Jeffrey Shallit), Acta Arith., 77 (1996), 77–96.
[132w] (Chairman of Working Party appointed by the National Committee for Mathematics of theAustralian Academy of Science) Mathematical Sciences: Adding to Australia (Australian Research Council, Discipline Research Strategies), (Canberra: Australian Government Publishing
Service, 1996), xxiii + 120 pp[132] ‘A comparative study of algorithms for computing continued fractions of algebraic numbers’,(with Richard P. Brent and Herman J. J. te Riele), in Henri Cohen ed., Algorithmic Number Theory (Proc. Second International Symposium, ANTS-II, Talence, France, May 1996),
Springer Lecture Notes in Computer Science 1122 (1996), 35–47.
[133a] ‘Divisibility sequences and other Hadamard problems’, International Conf. on Diophantine
Analysis and its Applications, in Honour of Acad. V. G. Sprindẑuk (1936–1987), Minsk (Belarus) September 1996, p25.
[133] ‘Beer and continued fractions with periodic period’, in Number Theory : Fifth Conference of theCanadian Number Theory Association, K. S. Williams and R. Gupta eds., CRM Proceedings
and Lecture Notes (Centre de Recherches Mathématiques, Montreal) 19 (1999), 309–314 [ISBN0-8218-0964-4].
[134] ‘On lacunary formal power series and their continued fraction expansion’, (with Michel Mendès
France and Jeffrey Shallit), in Number Theory in Progress (Proc. Conf. in honour of Andrzej
Schinzel on the occasion of his 60th birthday), K. Győry, H. Iwaniec and J. Urbanowicz eds,
Walter de Gruyter, Berlin 1999, 321–326.
[134`] ‘Pace Serge Lang’ (Letter to the Editor), CMS Notes 29 (9), December, 1997[135] ‘A powerful determinant’, Experimental Math., 10:2 (2001), 307–320.
[136] ‘Values of the Dedekind eta function at quadratic irrationalities’ (with Kenneth S. Williams),
Canad. J. Math., 51 (1999), 176–224; Corrigenda: ibid., 53 (2001), 434–448.

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[136f] Entries on ‘Fermat’s Last Theorem’, #249; ‘Skolem–Mahler–Lech Theorem’, #453, in Encyclopaedia of Mathematics, Supplement Volume I, Editor-in-Chief, Prof. dr. M. Hazewinkel(Kluwer Academic Publishers, 1997)[137] ‘Arithmetic properties of automata: regular sequences II’, manuscript in preparation.
[137r] Review of Kumiko Nishioka, Mahler Functions and Transcendence, Lecture Notes in Mathematics 1631 (Springer, 1996); in Bull. Lond. Math. Soc. 30 (1998), 663–664.
[138] ‘On the distribution of solutions of Thue’s equation’ (with B. Brindza, Á, Pintér, and M. Waldschmidt), in Number Theory in Progress (Proc. Conf. in honour of Andrzej Schinzel on theoccasion of his 60th birthday), K. Győry, H. Iwaniec and J. Urbanowicz eds, Walter de Gruyter,
Berlin 1999, 35–46.
[138r] ‘A proof that Euler missed . . . Apéry’s proof of the irrationality of ζ(3) ; An informal report’(The Mathematical Intelligencer 1 (1979), 195-203), reprinted in Pi: A source book , Lennart
Berggren, Jonathan Borwein and Peter Borwein eds., Springer-Verlag 1997, 439–447.
[139] ‘Zero testing of p-adic and modular polynomials’ (with Marek Karpinski and Igor Shparlinski),J. Theoretical Comp. Sc., 233 (2000), 309–317.
[140] ‘A note on Jacobi symbols and continued fractions’ (with P. G. Walsh), Amer. Math. Monthly,
106 (1999), 46–50.
[141] ‘Formal power series and their continued fraction expansion’, in Joe Buhler ed., Algorithmic
Number Theory (Proc. Third International Symposium, ANTS-III, Portland, Oregon, June1998), Springer Lecture Notes in Computer Science 1423 (1998), 358–371.
[141l] Speech in response on receiving a Dhc at Université Bordeaux I, January 8, 1998.
[142] ‘Continued fractions, Jacobi symbols and quadratic diophantine equations’ (with R. A. Mollin),
Canad. Math. Bulletin, 43 (2000), 218–225.
[142f] ‘La dimostrazione dell’ultimo teorema di Fermat’, in Enciclopedia Italiana, Appendice 2000,
Roma 2000, 341–344.
[143] Continued Fractions, book in preparation, one chapter completed,[144] ‘Reduction of continued fractions of formal power series’ in ‘Continued Fractions: From Analytic
Number Theory to Constructive Approximation’ (Columbia, Missouri May, 1998), Bruce Berndt
and Fritz Gesztesy eds., Contemporary Math. 236 (1999), 343–355.
[145] ‘Non-periodic continued fractions in hyperelliptic function fields’ (Dedicated to George Szekeres
on his 90th birthday), Bull. Austral. Math. Soc. 64 (2001), 331–343.
[146] ‘On periods of elements from real quadratic number fields’ (with Edward B. Burger), in Constructive, Experimental and Nonlinear Analysis (Limoges, 1999; in honour of Jonathan Borwein
Dhc), Michel Théra ed, CMS Conference Proceedings 27, Amer. Math. Soc., Providence, RI,
2000, 35–43.
[147f] Entry on ‘Fermat–Goss–Denis Theorem’, in Encyclopaedia of Mathematics, Supplement Volume2, Editor-in-Chief, Prof. dr. M. Hazewinkel (Kluwer Academic Publishers, 2000), pp217–218.
[147] ‘Simple zeros of polynomials in a recurrence sequence’ (with Ákos Pintér), manuscript in preparation, currently 3pp.
[148] ‘Computer verification of the Ankeny-Artin-Chowla conjecture for all primes less than 100 000 000 000(with Herman J. J. te Riele and Hugh C. Williams), Math. Comp., 70 (2001), 1311–1328.
[149c] ‘Quasi-elliptic integrals and periodic continued fractions’, Conference on Number Theory andits Applications (Chung-Li, Taiwan, October 14–16, 1999); conference abstracts, 47–61.
[149] ‘Quasi-elliptic integrals and periodic continued fractions’ (with Xuan Chuong Tran), Monatshefte Math., 131 (2000), 155-169.

A. J. van der Poorten — Manuscripts and Publications — July, 2007[150] Recurrence Sequences (Graham Everest, Alf van der Poorten, Igor Shparlinski, and Thomas
Ward), Mathematical Surveys and Monographs 104, American Mathematical Society 2003,
318pp. ISBN 0-8218-3387-1.
[151] ‘On Number Theory and Kustaa Inkeri’, in Number Theory (Proc. Turku Symposium on Number Theory in Memory of Kustaa Inkeri, Turku, May 31–June 4, 1999), Matti Jutila and Tauno
Metsänkylä eds., Walter de Gruyter, Berlin 2001, 281-292.
[152] ‘Algebraic independence of the derivatives of the period of the Carlitz module’ (with W. Dale
Brownawell), completed manuscript, 12pp.
[153] ‘Ideal constructions and irrationality measures of roots of algebraic numbers’ (with Paula Beazley Cohen), Illinois J. Math., 46.1 (2002), 63–80.
[154] ‘A note on NUCOMP’, Math. Comp., 72.244 (2003), 1935–1946.
[155] ‘The Hermite-Serret algorithm and 122 + 332 ’, Proc. Workshop on Cryptography and Computational Number Theory (CCNT’99), (National University of Singapore, 22-26 November, 1999),
K.-Y. Lam, I. E. Shparlinski, H. Wang and C. Xing eds., Birkhäuser 2001, 129–136.
[155`] ‘Voordeliger dan science fiction’ (Konrad Knopp, five Dover books on the Theory of Functions;in 1960 priced at US$1.35 per volume): ‘Welk wiskundeboek heeft in uw leven op u de meeste
indruk gemaakt?’ Nieuw Archiev voor Wiskunde, fijfde serie, 1 (Juni, 2000), 169–170.
[156] ‘Binary quadratic forms and the eta function’ (with Robin Chapman), in Number Theory for
the Millennium, Proc. Millennial Conf. Number Theory (Urbana, IL, May 21–26, 2000) (M. A.
Bennett et al., eds.), A K Peters, Boston, 2002, 215–227.
[156t] Japanese translation of Notes on Fermats Last Theorem by Itaru Yamaguchi, (Tokyo: Morikita,
2000), 285pp.
[157] ‘Symmetry and Folding’ (dedicated to Michel Mendès France on his 65th birthday), Jour.
Théorie des Nombres de Bordeaux , 14.2 (2002), 603–611.
[157r] Review of C. J. Mozzochi, The Fermat Diary, American Mathematical Society, Providence, RI,
2000. xii +196 pp. ISBN: 0-8218-2670-0; in Austral. Math. Soc. Gazette, 28.3 (2001), 164–165.
[158] ‘Periodic continued fractions in elliptic function fields’ (with Xuan Chuong Tran), in Claus
Fieker and David R. Kohel eds, Algorithmic Number Theory (Proc. Fifth International Symposium, ANTS-V, Sydney, NSW, Australia July 2002), Springer Lecture Notes in Computer
Science 2369 (2002), 390–404.
[158r] Review of Andrzej Schinzel (with an appendix by Umberto Zannier), Polynomials with special
regard to reducibility. Cambridge: Cambridge University Press, 2000. x +558 p., prijs £60,– (hc).
Encyclopedia of Mathematics and its Applications 77. ISBN 0-521-66225-7; in Nieuw Archiefv. Wiskunde 5e serie 2.3 (2001), 281–282.
[159] ’Squares from products of consecutive integers’ (with Gerhard J. Woeginger), Amer. Math.
Monthly, 109.5 (2002), 459–462.
[160] ‘Computational aspects of NUCOMP’ (with Michael J Jacobson Jr), in Claus Fieker and David
R. Kohel eds, Algorithmic Number Theory (Proc. Fifth International Symposium, ANTS-V,
Sydney, NSW, Australia July 2002), Springer Lecture Notes in Computer Science 2369 (2002),
120–133.
[161] ‘Life on the edge’, Amer. Math. Monthly, 109.9 (2002), 850–853.
[161d] Arthur Bertram Chandler (1912-1984), science fiction author, to appear in the Australian Dictionary of Biography, 17 (2007).
[162] ‘On the twin prime comjecture’ (with Teur Ah-Mah), The AustMS Gazette 31.1 (2004), 36–39.
[163] ‘Periodic continued fractions and elliptic curves’, in High Primes and Misdemeanours: lecturesin honour of the 60th birthday of Hugh Cowie Williams, Alf van der Poorten and Andreas Steineds., Fields Institute Communications 42, American Mathematical Society, 2004, 353–365.

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A. J. van der Poorten — Manuscripts and Publications — July, 2007[164] ‘Specialisation and reduction of continued fraction expansions of formal power series’ (to JeanLouis Nicolas on his 60th birthday), The Ramanujan J. 9 (2005), 83–91;
or see arXiv: math.NT/0403225.
[165] ‘Quadratic irrational integers with partly prescribed continued fraction expansion’ (in memoryof Professor Dr Bela Brindza), Publ. Math. Debrecen, 65.3-4 (2004), 481–496.
[166] ‘Integer Sequences and Periodic Points’ (with G. Everest, Y. Puri, and T. Ward), Journal of
Integer Sequences 5 , 02.2.3, (2002), 1–10.
[166c] ‘Corrigenda and addition to “Computer verification of the Ankeny-Artin-Chowla conjecture forall primes less than 100 000 000 000”’ (with Herman J. J. te Riele and Hugh C. Williams), Math.
Comp., 72.241 (2002), 521–523.
[167a] ‘Peer refereeing . . . will it be missed?’, in Fengshan Bai and Bernd Wegner eds. Electronic
Information and Communication in Mathematics, Springer Lecture Notes in Computer Science2730 (2003), 132–143.
[167b] ‘Three views of peer review’ (with Steven Krantz and Greg Kuperberg, in Notices of the American Mathematical Society, 50.6 (2003), 678–682.
[168] ‘Squares from products of integers’ (with William D Banks), The AustMS Gazette 31.1 (2004),
40–42.
[169] ‘Elliptic sequences and continued fractions’, Journal of Integer Sequences, 8 (2005), paper
05.2.5, 1–19; or see arXiv: math.NT/0403225.
[170e] (edited, with Andreas Stein) High Primes and Misdemeanours: lectures in honour of the 60thbirthday of Hugh Cowie Williams, Fields Institute Communications 42, American MathematicalSociety, 2004.
[171] ‘Jeepers, Creepers, . . . ’ (with Roger D. Patterson), in High Primes and Misdemeanours: lectures in honour of the 60th birthday of Hugh Cowie Williams, Alf van der Poorten and Andreas
Stein eds., Fields Institute Communications 42, American Mathematical Society, 2004, 305–316.
[171a] ‘Advice to Referees . . . ’ (with Andreas Stein), in High Primes and Misdemeanours: lectures inhonour of the 60th birthday of Hugh Cowie Williams, Alf van der Poorten and Andreas Steineds., Fields Institute Communications 42, American Mathematical Society, 2004, 391–392.
[172] ‘Curves of genus 2, continued fractions, and Somos sequences’, Journal of Integer Sequences, 8(2005), paper 05.3.4. 1–9; or see arXiv: math.NT/0412293.
[173] ‘Pseudo-elliptic integrals, units, and torsion’ (with Francesco Pappalardi), J. Austral. Math.
Soc. 79 (2005), 335–347; or see arXiv: math.NT/0403228.
[174] ‘A curious cubic identity and self-similar sums of squares’ (with Kurt Thomsen and Mark
Wiebe), to appear in The Math. Intelligencer , Spring 2007.
[174b] ‘Exactly one hundred nontrivial composites’, The AustMS Gazette 33.5 (2006), 326–327.
[175] ‘Recurrence relations for elliptic sequences: every Somos 4 is a Somos k’ (with Christine S.
Swart), to appear in Bull. London Math. Soc.; see arXiv: math.NT/0412293.
[175r] Review of Automatic Sequences by Jean-Paul Allouche and Jeffrey Shallit, Cambridge University Press, 2003; Math. Comp., 74.250, (2005), 1039–1040.
[176] ‘In thrall to Fibonacci’.
[177] ‘Characterization of a generalized Shanks sequence’ (with R. D. Patterson and H. C. Williams),
Pacific J. Math. 230.1 (2007), 185–215.
[178] ‘Hyperelliptic curves, continued fractions, and Somos sequences’, Proc. RIMS Conference on
Analytic Number Theory and Related Areas (Kyoto, October 18–22, 2004), RIMS August(2006), 98–107.

A. J. van der Poorten — Manuscripts and Publications — July, 2007[179] ‘Continued fractions and Somos sequences’, EURANDOM workshop on Dynamical Systems,
Probability Theory, and Statistical Mechanics , January 3–7, 2005; IMS Lecture Notes–Monograph
Series in Dynamics and Stochastics, 48 (2006), 212–224.
[180] ‘Determined sequences, continued fractions, and hyperelliptic curves’, Algorithmic Number Theory (Proc. Seventh International Symposium, ANTS 7, TU Berlin July 2006), Springer Lecture
Notes in Computer Science 4076 (2006), 393–405.
[180r] Review of ‘Introduction to Modern Number Theory’, by Yu. I. Manin and A. A. Panchishkin,
2nd Edition; AustMS Gazette 34.1 (2007), 47–48.
[181] ‘Sequences of Jacobian varieties with torsion divisors of quadratic order’ (with R. D. Patterson
and H. C. Williams).
[183] ‘Fermat’s four squares theorem’.

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