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
* 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

### 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)
* Andrews-Askey 積分
* q-Dyson 予想を提唱
*Gordon-Andrews 恒等式

## 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
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