ジョージ・アンドリューズ

ジョージ・アンドリューズ 2009

ジョージ・アンドリューズ（英語: George Andrews、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

• ${\displaystyle q}$-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

→「ロジャーズ＝ラマヌジャン恒等式」も参照

共著

• A simple proof of Ramanujan’s summation of the ${\displaystyle _{1}\psi _{1}}$, GE Andrews, R Askey - Aequationes Mathematicae, 1978.

1980年代

• Another ${\displaystyle q}$-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 ${\displaystyle A_{2}}$ 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.
• ${\displaystyle q}$-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.
• ${\displaystyle q}$-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 ${\displaystyle q}$-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 ${\displaystyle q}$-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 ${\displaystyle q}$-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 ${\displaystyle q}$-trinomial coefficients, GE Andrews - Journal of the American Mathematical Society, 1990.
• ${\displaystyle q}$-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 ${\displaystyle n}$, 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)[1][2][3][4][5][6]
• Andrews-Askey 積分[7][8][9]
• ${\displaystyle q}$-Dyson 予想を提唱[10][11]
• Gordon-Andrews 恒等式[12][13][14][15][16][17][18]

出典

1. Andrews, G. E. (2004). On a partition function of Richard Stanley. The electronic journal of combinatorics, 11(2).
2. Ishikawa, M., & Zeng, J. (2009). The Andrews–Stanley partition function and Al-Salam–Chihara polynomials. Discrete Mathematics, 309(1), 151-175.
3. Yee, A. J. (2004). On partition functions of Andrews and Stanley. Journal of Combinatorial Theory, Series A, 107(2), 313-321.
4. 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.
5. 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.
6. Swisher, H. (2011). The Andrews-Stanley partition function and ${\displaystyle p(n)}$: congruences. Proceedings of the American Mathematical Society, 139(4), 1175-1185.
7. Wang, M. (2008). A remark on Andrews–Askey integral. Journal of Mathematical Analysis and Applications, 341(2), 1487-1494.
8. Cao, J. (2014). A note on generalized ${\displaystyle q}$-difference equations for ${\displaystyle q}$-beta and Andrews–Askey integral. Journal of Mathematical Analysis and Applications, 412(2), 841-851.
9. 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.
10. Bressoud, D., & Zeilberger, D. (1985). A proof of Andrews' ${\displaystyle q}$-Dyson conjecture. NUMBER THEORY AND RELATED TOPICS, 35.
11. Kadell, K. W. (1985). A proof of Andrews’ ${\displaystyle q}$-Dyson conjecture for 𝑛= 4. Transactions of the American Mathematical Society, 290(1), 127-144.
12. 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.
13. Melzer, E. (1994). Supersymmetric analogs of the Gordon-Andrews identities, and related TBA systems. arXiv preprint hep-th/9412154.
14. Warnaar, S. O. (1997). The Andrews–Gordon identities and ${\displaystyle q}$-multinomial coefficients. Communications in mathematical physics, 184(1), 203-232.
15. 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.
16. Berkovich, A., & Paule, P. (2001). Variants of the Andrews-Gordon identities. The Ramanujan Journal, 5(4), 391-404.
17. Hikami, K. (2006). ${\displaystyle q}$-series and ${\displaystyle L}$-functions related to half-derivatives of the Andrews-Gordon identity. The Ramanujan Journal, 11(2), 175-197.
18. Berkovich, A., & Paule, P. (2001). Lattice paths, ${\displaystyle q}$-multinomials and two variants of the Andrews-Gordon identities. The Ramanujan Journal, 5(4), 409-425.

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

• ジョージ・アンドリューズ - Mathematics Genealogy Project
• ジョージ・アンドリューズの出版物 - ResearchGate
• ジョージ・アンドリューズの出版物 - Google Scholar
• George E. Andrews - DBLP Bibliography Server