ジョージ・アンドリューズ

特殊関数・数論 (特に自然数の分割など) を専門とするアメリカ合衆国の数学者

ジョージ・アンドリューズ英語: George Andrews1938年12月4日 - )は特殊関数数論(特に自然数の分割など)を専門とするアメリカ合衆国の数学者である。

著書編集

関連文献編集

  • 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.

代表的な論文編集

共著編集

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

1980年代編集

  • 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年代編集

  • 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年代以降編集

  • 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.

単著編集

1960年代編集

  • 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年代編集

  • 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年代編集

  • 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年代以降編集

  • 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.

解説記事編集

  • 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.

主な業績編集

出典編集

  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  : 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  -difference equations for  -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'  -Dyson conjecture. NUMBER THEORY AND RELATED TOPICS, 35.
  11. ^ Kadell, K. W. (1985). A proof of Andrews’  -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  -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).  -series and  -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,  -multinomials and two variants of the Andrews-Gordon identities. The Ramanujan Journal, 5(4), 409-425.

関連項目編集

外部リンク編集