ジョージ・アンドリューズ

ジョージ・アンドリューズ（、1938年12月4日 - ）は、アメリカ合衆国の数学者。専門は、特殊関数・数論（特に自然数の分割など）。

 著書 
 -Series: Their Development and Application in Analysis, Number Theory, Combinatorics, Physics and Computer Algebra: Their Development and Application in Analysis, Number Theory, Combinatorics, Physics, and Computer Algebra, GE Andrews - 1986.
 Ramanujan revisited, GE Andrews - 1988 (:en:Academic Press)
 Number Theory (Dover, 1994, ISBN 0-486-68252-8)
 The Theory of Partitions (:en:Cambridge University Press, 1998, ISBN 0-521-63766-X)
 Integer Partitions (with Eriksson, Kimmo) (:en:Cambridge University Press, 2004, ISBN 0-521-84118-6)
 Ramanujan's Lost Notebook: Part I (with Bruce C. Berndt) (Springer, 2005, ISBN 0-387-25529-X)
 Ramanujan's Lost Notebook: Part II, (with Bruce C. Berndt) (Springer, 2008, ISBN 978-0-387-77765-8)
 Ramanujan's Lost Notebook: Part III, (with Bruce C. Berndt) (Springer, 2012, ISBN 978-1-4614-3809-0)
 Ramanujan's Lost Notebook: Part IV, (with Bruce C. Berndt) (Springer, 2013, ISBN 978-1-4614-4080-2)
 "Special functions" by George Andrews, Richard Askey, and Ranjan Roy, Encyclopedia of Mathematics and Its Applications, :en:Cambridge University Press, 1999.

 関連文献 
 Selected Works of George E Andrews (World Scientific Publishing, 2012, ISBN 978-1-84816-666-0)
 Askey, R. (2001). The work of George Andrews: a Madison perspective. In The Andrews Festschrift (pp. 17-38). Springer, Berlin, Heidelberg.

 代表的な論文 

共著
 A simple proof of Ramanujan’s summation of the , GE Andrews, R Askey - Aequationes Mathematicae, 1978.

 1980年代 
 Another -extension of the beta function, GE Andrews, R Askey - Proceedings of the American Mathematical Society, 1981.
 Eight-vertex SOS model and generalized Rogers-Ramanujan-type identities, GE Andrews, RJ Baxter, PJ Forrester - Journal of Statistical Physics, 1984.
 The Bailey lattice, AK Agarwal, GE Andrews, DM Bressoud - The Journal of the Indian Mathematical Society, 1987.
 Rogers-Ramanujan identities for partitions with “N copies of N”, AK Agarwal, GE Andrews - Journal of Combinatorial Theory, Series A, 1987.
 Partitions and indefinite quadratic forms, GE Andrews, FJ Dyson, D Hickerson - Inventiones Mathematicae, 1988.

 1990年代 
 The continued fractions found in the unorganized portions of Ramanujan's notebooks, GE Andrews, BC Berndt, L Jacobsen, RL Lamphere - 1992.
 Generalizations and refinements of a partition theorem of Gollnitz, K Alladi, GE Andrews, B Gordon - Journal fur die Reine und Angewandte Mathematik, 1995.
 An  Bailey lemma and Rogers-Ramanujan-type identities, G Andrews, A Schilling, S Warnaar - Journal of the American Mathematical Society, 1999.

 2000年代以降 
 An infinite family of Engel expansions of Rogers–Ramanujan type, GE Andrews, A Knopfmacher, P Paule - Advances in Applied Mathematics, 2000.
 MacMahon's partition analysis: the Omega package, GE Andrews, P Paule, A Riese - European Journal of Combinatorics, 2001.
 -series identities and values of certain L-functions, GE Andrews, J Jiménez-Urroz, K Ono - Duke Mathematical Journal, 2001.
 The WP-Bailey tree and its implications, G Andrews, A Berkovich - Journal of the London Mathematical Society, 2002.
 Baxter algebras and Hopf algebras, G Andrews, L Guo, W Keigher, K Ono - Transactions of the American Mathematical Society, 2003.
 A combinatorial interpretation of the Legendre-Stirling numbers, G Andrews, L Littlejohn - Proceedings of the American Mathematical Society, 2009
 Arithmetic properties of partitions with even parts distinct, GE Andrews, MD Hirschhorn, JA Sellers - The Ramanujan Journal, 2010.

 単著 
 1960年代 
 A simple proof of Jacobi’s triple product identity, GE Andrews - Proceedings of the American Mathematical Society, 1965.
 -identities of Auluck, Carlitz, and Rogers, GE Andrews - Duke Mathematical Journal, 1966.
 On the theorems of Watson and Dragonette for Ramanujan's mock theta functions, GE Andrews - American Journal of Mathematics, 1966.
 An analytic proof of the Rogers-Ramanujan-Gordon identities, GE Andrews - American Journal of Mathematics, 1966.
 A generalization of the Göllnitz-Gordon partition theorems, GE Andrews - Proceedings of the American Mathematical Society, 1967.
 On -difference equations for certain well-poised basic hypergeometric series, GE Andrews - The Quarterly Journal of Mathematics, 1968.

 1970年代 
 On a transformation of bilateral series with applications, GE Andrews - Proceedings of the American Mathematical Society, 1970.
 A polynomial identity which implies the Rogers-Ramanujan identities, GE Andrews - Scripta Math, 1970.
 Summations and transformations for basic Appell series, GE Andrews - Journal of the London Mathematical Society, 1972.
 Two theorems of Gauss and allied identities proved arithmetically, G Andrews - Pacific Journal of Mathematics, 1972.
 On the -analog of Kummer’s theorem and applications, GE Andrews - Duke Math. J, 1973.
 An analytic generalization of the Rogers-Ramanujan identities for odd moduli, GE Andrews - Proceedings of the National Academy of Sciences, 1974.
 On -analogues of the Watson and Whipple summations, GE Andrews - SIAM Journal on Mathematical Analysis, 1976.
 Partitions and Durfee dissection, GE Andrews - American Journal of Mathematics, 1979.

 1980年代 
 The hard-hexagon model and Rogers—Ramanujan type identities, GE Andrews - Proceedings of the National Academy of Sciences, 1981.
 Multiple series Rogers-Ramanujan type identities, G Andrews - Pacific journal of mathematics, 1984.
 The fifth and seventh order mock theta functions, GE Andrews - Transactions of the American Mathematical Society, 1986.

 1990年代以降 
 Euler’s “exemplum memorabile inductionis fallacis” and -trinomial coefficients, GE Andrews - Journal of the American Mathematical Society, 1990.
 -analogs of the binomial coefficient congruences of Babbage, Wolstenholme and Glaisher, GE Andrews - Discrete mathematics, 1999.
 Partitions, Durfee symbols, and the Atkin–Garvan moments of ranks, GE Andrews - Inventiones Mathematicae, 2007.
 The number of smallest parts in the partitions of , GE Andrews - Journal für die reine und angewandte Mathematik, 2008.

 解説記事 
 Sieves in the theory of partitions, GE Andrews - American Journal of Mathematics, 1972.
 Applications of basic hypergeometric functions, GE Andrews - SIAM Review, 1974.
 An introduction to Ramanujan's “lost” notebook, GE Andrews - The American Mathematical Monthly, 1979.
 Partitions: yesterday and today, GE Andrews - New Zealand Mathematical Society, 1979.

 主な業績 
 Andrews–Stanley 分割関数 (partition function)Andrews, G. E. (2004). On a partition function of Richard Stanley. The electronic journal of combinatorics, 11(2).Ishikawa, M., & Zeng, J. (2009). The Andrews–Stanley partition function and Al-Salam–Chihara polynomials. Discrete Mathematics, 309(1), 151-175.Yee, A. J. (2004). On partition functions of Andrews and Stanley. Journal of Combinatorial Theory, Series A, 107(2), 313-321.Sills, A. V. (2004). A combinatorial proof of a partition identity of Andrews and Stanley. International Journal of Mathematics and Mathematical Sciences, 2004(47), 2495-2501.Berkovich, A., & Garvan, F. (2006). On the Andrews-Stanley refinement of Ramanujan’s partition congruence modulo 5 and generalizations. Transactions of the American Mathematical Society, 358(2), 703-726.Swisher, H. (2011). The Andrews-Stanley partition function and : congruences. Proceedings of the American Mathematical Society, 139(4), 1175-1185.
 Andrews-Askey 積分Wang, M. (2008). A remark on Andrews–Askey integral. Journal of Mathematical Analysis and Applications, 341(2), 1487-1494.Cao, J. (2014). A note on generalized -difference equations for -beta and Andrews–Askey integral. Journal of Mathematical Analysis and Applications, 412(2), 841-851.Liu, Z. G. (2016). Extensions of Ramanujan's reciprocity theorem and the Andrews–Askey integral. Journal of Mathematical Analysis and Applications, 443(2), 1110-1129.
 -Dyson 予想を提唱Bressoud, D., & Zeilberger, D. (1985). A proof of Andrews' -Dyson conjecture. NUMBER THEORY AND RELATED TOPICS, 35.Kadell, K. W. (1985). A proof of Andrews’ -Dyson conjecture for 𝑛= 4. Transactions of the American Mathematical Society, 290(1), 127-144.
Gordon-Andrews 恒等式Capparelli, S., Lepowsky, J., & Milas, A. (2006). The Rogers–Selberg recursions, the Gordon–Andrews identities and intertwining operators. The Ramanujan Journal, 12(3), 379-397.Melzer, E. (1994). Supersymmetric analogs of the Gordon-Andrews identities, and related TBA systems. arXiv preprint hep-th/9412154.Warnaar, S. O. (1997). The Andrews–Gordon identities and -multinomial coefficients. Communications in mathematical physics, 184(1), 203-232.Richmond, B., & Szekeres, G. (1981). Some formulas related to dilogarithms, the zeta function and the Andrews-Gordon identities. Journal of the Australian Mathematical Society, 31(3), 362-373.Berkovich, A., & Paule, P. (2001). Variants of the Andrews-Gordon identities. The Ramanujan Journal, 5(4), 391-404.Hikami, K. (2006). -series and -functions related to half-derivatives of the Andrews-Gordon identity. The Ramanujan Journal, 11(2), 175-197.Berkovich, A., & Paule, P. (2001). Lattice paths, -multinomials and two variants of the Andrews-Gordon identities. The Ramanujan Journal, 5(4), 409-425.

 出典 

 関連項目 
 リチャード・アスキー
 アメリカ数学会（2009年に会長を務めている）

 外部リンク 





Category:アメリカ合衆国の数論学者
Category:特殊関数
381204
-381204
Category:米国科学アカデミー会員
Category:アメリカ数学会フェロー
Category:SIAMフェロー
Category:オレゴン州の数学者
Category:数学に関する記事
Category:1938年生
Category:存命人物