ジョージ・アンドリューズ

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

$q$ -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.

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 $_{1}\psi _{1}$ , GE Andrews, R Askey - Aequationes Mathematicae, 1978.

1980年代

Another $q$ -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 $A_{2}$ 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.
$q$ -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.
$q$ -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 $q$ -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 $q$ -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 $q$ -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 $q$ -trinomial coefficients, GE Andrews - Journal of the American Mathematical Society, 1990.
$q$ -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 $n$ , 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]
$q$ -Dyson 予想を提唱^[10]^[11]
Gordon-Andrews 恒等式^[12]^[13]^[14]^[15]^[16]^[17]^[18]

出典

^ 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 $p(n)$ : congruences. Proceedings of the American Mathematical Society, 139(4), 1175-1185.
^ 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 $q$ -difference equations for $q$ -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.
^ Bressoud, D., & Zeilberger, D. (1985). A proof of Andrews' $q$ -Dyson conjecture. NUMBER THEORY AND RELATED TOPICS, 35.
^ Kadell, K. W. (1985). A proof of Andrews’ $q$ -Dyson conjecture for 𝑛= 4. Transactions of the American Mathematical Society, 290(1), 127-144.
^ 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 $q$ -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). $q$ -series and $L$ -functions related to half-derivatives of the Andrews-Gordon identity. The Ramanujan Journal, 11(2), 175-197.
^ Berkovich, A., & Paule, P. (2001). Lattice paths, $q$ -multinomials and two variants of the Andrews-Gordon identities. The Ramanujan Journal, 5(4), 409-425.

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

この項目は、数学者に関連した書きかけの項目です。この項目を加筆・訂正などしてくださる協力者を求めています（プロジェクト:人物伝／Portal:自然科学）。

[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 $p(n)$ : 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 $q$ -difference equations for $q$ -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' $q$ -Dyson conjecture. NUMBER THEORY AND RELATED TOPICS, 35.

[11] Kadell, K. W. (1985). A proof of Andrews’ $q$ -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 $q$ -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). $q$ -series and $L$ -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, $q$ -multinomials and two variants of the Andrews-Gordon identities. The Ramanujan Journal, 5(4), 409-425.

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表話編歴数論の主要なトピック
分野	整数論代数的整数論解析的整数論幾何学的数論（英語版）計算数論超越数論（英語版）組合せ論的整数論（英語版）数論幾何学数論トポロジー数論力学
主要概念	数自然数素数有理数無理数代数的数超越数 $p$ 進数算術合同算術数論的関数
諸概念	二次形式モジュラー形式 L関数ディオファントス方程式ディオファントス近似連分数
日本人研究者	伊原康隆織田孝幸加藤和也斎藤秀司斎藤毅黒川信重志村五郎佐藤幹夫辻雄
海外の研究者	シュリニヴァーサ・ラマヌジャンテレンス・タオジョージ・アンドリューズ
数論のトピック一覧（英語版）（娯楽（英語版））年表カテゴリ

表話編歴アメリカ数学会会長
1888–1900	en:John Howard Van Amringe (1888–1890) en:Emory McClintock (1891–1894) ジョージ・ウィリアム・ヒル (1895–1896) サイモン・ニューカム (1897–1898) en:Robert Simpson Woodward (1899–1900)
1901–1924	E・H・ムーア (1901–1902) en:Thomas Fiske (1903–1904) en:William Fogg Osgood (1905–1906) en:Henry Seely White (1907–1908) en:Maxime Bôcher (1909–1910) en:Henry Burchard Fine (1911–1912) en:Edward Burr Van Vleck (1913–1914) アーネスト・ウィリアム・ブラウン (1915–1916) レオナード・E・ディクソン (1917–1918) en:Frank Morley (1919–1920) en:Gilbert Ames Bliss (1921–1922) オズワルド・ヴェブレン (1923–1924)
1925–1950	ジョージ・デビット・バーコフ (1925–1926) en:Virgil Snyder (1927–1928) en:Earle Raymond Hedrick (1929–1930) en:Luther P. Eisenhart (1931–1932) en:Arthur Byron Coble (1933–1934) ソロモン・レフシェッツ (1935–1936) en:Robert Lee Moore (1937–1938) en:Griffith C. Evans (1939–1940) en:Marston Morse (1941–1942) マーシャル・ストーン (1943–1944) en:Theophil Henry Hildebrandt (1945–1946) en:Einar Hille (1947–1948) en:Joseph L. Walsh (1949–1950)
1951–1974	ジョン・フォン・ノイマン (1951–1952) en:Gordon Thomas Whyburn (1953–1954) en:Raymond Louis Wilder (1955–1956) en:Richard Brauer (1957–1958) en:Edward J. McShane (1959–1960) en:Deane Montgomery (1961–1962) ジョゼフ・L・ドゥーブ (1963–1964) en:Abraham Adrian Albert (1965–1966) en:Charles B. Morrey Jr. (1967–1968) オスカー・ザリスキ (1969–1970) en:Nathan Jacobson (1971–1972) ソーンダース・マックレーン (1973–1974)
1975–2000	en:Lipman Bers (1975–1976) アーエイチ・ビング (1977–1978) ピーター・ラックス (1979–1980) en:Andrew M. Gleason (1981–1982) ジュリア・ロビンソン (1983–1984) en:Irving Kaplansky (1985–1986) ジョージ・モストウ (1987–1988) William Browder (1989–1990) ミハイル・アルティン (1991–1992) ロナルド・グラハム (1993–1994) en:Cathleen Synge Morawetz (1995–1996) en:Arthur Jaffe (1997–1998) en:Felix Browder (1999–2000)
2001–2024	en:Hyman Bass (2001–2002) en:David Eisenbud (2003–2004) ジェームズ・アーサー (2005–2006) en:James Glimm (2007–2008) ジョージ・アンドリューズ (2009–2010) en:Eric Friedlander (2011–2012) en:David Vogan (2013–2014) Robert Bryant (2015–2016) ケン・リベット (2017–2018) en:Jill Pipher (2019–2020) en:Ruth Charney (2021–2022) en:Bryna Kra (2023–2024)

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ジョージ・アンドリューズ

著書

関連文献

代表的な論文

共著

1980年代

1990年代

2000年代以降

単著

1960年代

1970年代

1980年代

1990年代以降

解説記事

主な業績

出典

関連項目

外部リンク