Format:
vii, 124 Seiten
ISBN:
9781470454333
Series Statement:
Memoirs of the American Mathematical Society volume 280, number 1382 (November 2022)
Content:
"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"--
Note:
"November 2022, volume 280, number 1382 (fifth of 8 numbers)"
,
Includes bibliographical references and index
Additional Edition:
ISBN 9781470472825
Additional Edition:
Erscheint auch als Online-Ausgabe Fuselier, Jenny Hypergeometric functions over finite fields Providence, RI : American Mathematical Society, 2022 ISBN 9781470472825
Additional Edition:
Erscheint auch als Online-Ausgabe Fuselier, Jenny Hypergeometric Functions over Finite Fields Providence : American Mathematical Society, 2022 ISBN 9781470472825
Language:
English
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