ジョージ・アンドリューズ

ジョージ・アンドリューズは、アメリカ合衆国の数学者。専門は、特殊関数・数論。

1. 著書
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-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 
Number Theory 
The Theory of Partitions 
Integer Partitions  
Ramanujan's Lost Notebook: Part I  
Ramanujan's Lost Notebook: Part II,  
Ramanujan's Lost Notebook: Part III,  
Ramanujan's Lost Notebook: Part IV,  
"Special functions" by George Andrews, Richard Askey, and Ranjan Roy, Encyclopedia of Mathematics and Its Applications, :en:Cambridge University Press, 1999.

2. 関連文献
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Selected Works of George E Andrews 
Askey, R. . The work of George Andrews: a Madison perspective. In The Andrews Festschrift . Springer, Berlin, Heidelberg.

3. 代表的な論文
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3.1. 共著
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A simple proof of Ramanujan’s summation of the , GE Andrews, R Askey - Aequationes Mathematicae, 1978.

3.1.1. 1980年代
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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.

3.1.2. 1990年代
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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.

3.1.3. 2000年代以降
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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.

3.2. 単著
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3.2.1. 1960年代
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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.

3.2.2. 1970年代
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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.

3.2.3. 1980年代
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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.

3.2.4. 1990年代以降
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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.

4. 解説記事
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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.

5. 主な業績
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Andrews–Stanley 分割関数 
Andrews-Askey 積分
-Dyson 予想を提唱
Gordon-Andrews 恒等式

6. 出典
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7. 関連項目
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リチャード・アスキー
アメリカ数学会

8. 外部リンク
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