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Hypergeometric functions over finite fields
Building on the developments of many people including Evans, Greene, Katz, McCarthy, Ono, Roberts, and Rodriguez-Villegas, we consider period functions for hypergeometric type algebraic varieties over finite fields and consequently study hypergeometric functions over finite fields in a manner that i...
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| Main Authors : | , , , , |
|---|---|
| Format : | Book |
| Language : | anglais |
| Title statement : | Hypergeometric functions over finite fields / Jenny Fuselier, Ling Long, Ravi Ramakrishna, Holly Swisher, Fang-Ting Tu |
| Published : |
Providence (R.I.) :
American Mathematical Society
, 2022 |
| Physical Description : | 1 vol. (VII-124 p.) |
| Series : | Memoirs of the American Mathematical Society ; 1382 |
| Subjects : |
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| 200 | 1 | |a Hypergeometric functions over finite fields |f Jenny Fuselier, Ling Long, Ravi Ramakrishna, Holly Swisher, Fang-Ting Tu | |
| 214 | 0 | |a Providence (R.I.) |c American Mathematical Society |d 2022 | |
| 215 | |a 1 vol. (VII-124 p.) |c fig. |d 26 cm | ||
| 225 | 0 | |a Memoirs of the American Mathematical Society |v number 1382 | |
| 300 | |a "November 2022, volume 280, number 1382 (fifth of 8 numbers)" | ||
| 320 | |a Bibliogr. p. 117-121. Index | ||
| 330 | |a Building on the developments of many people including Evans, Greene, Katz, McCarthy, Ono, Roberts, and Rodriguez-Villegas, we consider period functions for hypergeometric type algebraic varieties over finite fields and consequently study hypergeometric functions over finite fields in a manner that is parallel to that of the classical hypergeometric functions. Using a comparison between the classical gamma function and its finite field analogue the Gauss sum, we give a systematic way to obtain certain types of hypergeometric transformation and evaluation formulas over finite fields and interpret them geometrically using a Galois representation perspective. As an application, we obtain a few finite field analogues of algebraic hypergeometric identities, quadratic and higher transformation formulas, and evaluation formulas. We further apply these finite field formulas to compute the number of rational points of certain hypergeometric varieties. |2 résumé des auteurs | ||
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