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...
Gespeichert in:
| Hauptverfasser: | , , , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Mathematical Society
2022
|
| Schriftenreihe: | Memoirs of the American Mathematical Society
Volume 280, Number 1382 (fifth of 8 numbers) |
| Schlagworte: | |
| Zusammenfassung: | "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"-- |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | vii, 124 Seiten |
| ISBN: | 9781470454333 |
Internformat
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| 100 | 1 | |a Fuselier, Jenny |0 (DE-588)1299393381 |4 aut | |
| 245 | 1 | 0 | |a Hypergeometric functions over finite fields |c Jenny Fuselier ; Ling Long ; Ravi Ramakrishna ; Holly Swisher ; Fang-Ting Tu |
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c 2022 | |
| 264 | 4 | |c © 2022 | |
| 300 | |a vii, 124 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society |v Volume 280, Number 1382 (fifth of 8 numbers) | |
| 500 | |a Includes bibliographical references and index | ||
| 520 | 3 | |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"-- | |
| 653 | 0 | |a Finite fields (Algebra) | |
| 653 | 0 | |a Hypergeometric functions | |
| 653 | 0 | |a Number theory -- Finite fields and commutative rings (number-theoretic aspects) -- Exponential sums | |
| 653 | 0 | |a Number theory -- Finite fields and commutative rings (number-theoretic aspects) -- Other character sums and Gauss sums | |
| 653 | 0 | |a Special functions -- Hypergeometric functions -- Classical hypergeometric functions, $_ | |
| 653 | 0 | |a Special functions -- Hypergeometric functions -- Generalized hypergeometric series, $_ | |
| 653 | 0 | |a Number theory -- Discontinuous groups and automorphic forms -- Galois representations | |
| 653 | 0 | |a Number theory -- Algebraic number theory: local and $p$-adic fields -- Zeta functions and $L$-functions | |
| 700 | 1 | |a Ling, Long |d 1962- |0 (DE-588)12198334X |4 aut | |
| 700 | 1 | |a Ramakrishna, Ravi Kumar |0 (DE-588)1299393551 |4 aut | |
| 700 | 1 | |a Swisher, Holly |0 (DE-588)1299393853 |4 aut | |
| 700 | 1 | |a Tu, Fang-Ting |0 (DE-588)129939406X |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4704-7282-5 |
| 830 | 0 | |a Memoirs of the American Mathematical Society |v Volume 280, Number 1382 (fifth of 8 numbers) |w (DE-604)BV008000141 |9 1382 | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-034058858 | ||
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| author | Fuselier, Jenny Ling, Long 1962- Ramakrishna, Ravi Kumar Swisher, Holly Tu, Fang-Ting |
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| author_facet | Fuselier, Jenny Ling, Long 1962- Ramakrishna, Ravi Kumar Swisher, Holly Tu, Fang-Ting |
| author_role | aut aut aut aut aut |
| author_sort | Fuselier, Jenny |
| author_variant | j f jf l l ll r k r rk rkr h s hs f t t ftt |
| building | Verbundindex |
| bvnumber | BV048684551 |
| ctrlnum | (OCoLC)1365607101 (DE-599)KXP1832134202 |
| dewey-full | 512.7/4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.7/4 |
| dewey-search | 512.7/4 |
| dewey-sort | 3512.7 14 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| id | DE-604.BV048684551 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T21:26:11Z |
| indexdate | 2024-07-10T09:46:02Z |
| institution | BVB |
| isbn | 9781470454333 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-034058858 |
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| physical | vii, 124 Seiten |
| publishDate | 2022 |
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| publisher | American Mathematical Society |
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| series | Memoirs of the American Mathematical Society |
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| spelling | Fuselier, Jenny (DE-588)1299393381 aut Hypergeometric functions over finite fields Jenny Fuselier ; Ling Long ; Ravi Ramakrishna ; Holly Swisher ; Fang-Ting Tu Providence, RI American Mathematical Society 2022 © 2022 vii, 124 Seiten txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society Volume 280, Number 1382 (fifth of 8 numbers) Includes bibliographical references and index "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"-- Finite fields (Algebra) Hypergeometric functions Number theory -- Finite fields and commutative rings (number-theoretic aspects) -- Exponential sums Number theory -- Finite fields and commutative rings (number-theoretic aspects) -- Other character sums and Gauss sums Special functions -- Hypergeometric functions -- Classical hypergeometric functions, $_ Special functions -- Hypergeometric functions -- Generalized hypergeometric series, $_ Number theory -- Discontinuous groups and automorphic forms -- Galois representations Number theory -- Algebraic number theory: local and $p$-adic fields -- Zeta functions and $L$-functions Ling, Long 1962- (DE-588)12198334X aut Ramakrishna, Ravi Kumar (DE-588)1299393551 aut Swisher, Holly (DE-588)1299393853 aut Tu, Fang-Ting (DE-588)129939406X aut Erscheint auch als Online-Ausgabe 978-1-4704-7282-5 Memoirs of the American Mathematical Society Volume 280, Number 1382 (fifth of 8 numbers) (DE-604)BV008000141 1382 |
| spellingShingle | Fuselier, Jenny Ling, Long 1962- Ramakrishna, Ravi Kumar Swisher, Holly Tu, Fang-Ting Hypergeometric functions over finite fields Memoirs of the American Mathematical Society |
| title | Hypergeometric functions over finite fields |
| title_auth | Hypergeometric functions over finite fields |
| title_exact_search | Hypergeometric functions over finite fields |
| title_exact_search_txtP | Hypergeometric functions over finite fields |
| title_full | Hypergeometric functions over finite fields Jenny Fuselier ; Ling Long ; Ravi Ramakrishna ; Holly Swisher ; Fang-Ting Tu |
| title_fullStr | Hypergeometric functions over finite fields Jenny Fuselier ; Ling Long ; Ravi Ramakrishna ; Holly Swisher ; Fang-Ting Tu |
| title_full_unstemmed | Hypergeometric functions over finite fields Jenny Fuselier ; Ling Long ; Ravi Ramakrishna ; Holly Swisher ; Fang-Ting Tu |
| title_short | Hypergeometric functions over finite fields |
| title_sort | hypergeometric functions over finite fields |
| volume_link | (DE-604)BV008000141 |
| work_keys_str_mv | AT fuselierjenny hypergeometricfunctionsoverfinitefields AT linglong hypergeometricfunctionsoverfinitefields AT ramakrishnaravikumar hypergeometricfunctionsoverfinitefields AT swisherholly hypergeometricfunctionsoverfinitefields AT tufangting hypergeometricfunctionsoverfinitefields |