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010 a| 2022048388;

020 a| 9781470454333q| (paperback);

020 z| 9781470472825q| (epub);

035 a| (WaSeSS)ssj0002763418;

042 a| pcc;

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084 a| 11T23a| 11T24a| 33C05a| 33C20a| 11F80a| 11S402| msc;

100 1 a| Fuselier, Jenny.?| UNAUTHORIZED;

245 10 a| Hypergeometric functions over finite fieldsh| [electronic resource] /c| Jenny Fuselier, Ling Long, Ravi Ramakrishna, Holly Swisher, Fang-Ting Tu.;

260 a| Providence, RI :b| American Mathematical Society,c| [2022];

300 a| vii, 124 pages :b| illustrations ;c| 26 cm.;

490 0 a| Memoirs of the American Mathematical Society ;v| number 1382;

504 a| Includes bibliographical references (page 117-121) and index.;

506 a| Available only to authorized users.;

520 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"--c| Provided by publisher.;

538 a| Mode of access: World Wide Web;

650 0 a| Finite fields (Algebra)=| ^A72195;

650 0 a| Hypergeometric functions.=| ^A377048;

650 7 a| Number theory -- Finite fields and commutative rings (number-theoretic aspects) -- Exponential sums.2| msc;

650 7 a| Number theory -- Finite fields and commutative rings (number-theoretic aspects) -- Other character sums and Gauss sums.2| msc;

650 7 a| Special functions -- Hypergeometric functions -- Classical hypergeometric functions, $.2| msc;

650 7 a| Special functions -- Hypergeometric functions -- Generalized hypergeometric series, $.2| msc;

650 7 a| Number theory -- Discontinuous groups and automorphic forms -- Galois representations.2| msc;

650 7 a| Number theory -- Algebraic number theory: local and $p$-adic fields -- Zeta functions and $L$-functions.2| msc;

655 0 a| Electronic books.=| ^A491897;

700 1 a| Long, Lingc| (Professor of mathematics)?| UNAUTHORIZED;

700 1 a| Ramakrishna, Ravi Kumar.?| UNAUTHORIZED;

700 1 a| Swisher, Holly.?| UNAUTHORIZED;

700 1 a| Tu, Fang-Ting.?| UNAUTHORIZED;

856 40 z| Full text available from Ebook Central - Academic Completeu| https://ebookcentral.proquest.com/lib/eastcarolina/detail.action?docID=30222575;

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Hypergeometric functions over finite fields / Jenny Fuselier, Ling Long, Ravi Ramakrishna, Holly Swisher, Fang-Ting Tu.

Author/creator	Fuselier, Jenny
Format	Electronic
Publication Info	Providence, RI : American Mathematical Society, [2022]
Description	vii, 124 pages : illustrations ; 26 cm.
Supplemental Content	Full text available from Ebook Central - Academic Complete
Subjects	Finite fields (Algebra) Hypergeometric functions.

Other author/creator	Long, Ling (Professor of mathematics)
Other author/creator	Ramakrishna, Ravi Kumar.
Other author/creator	Swisher, Holly.
Other author/creator	Tu, Fang-Ting.
Series	Memoirs of the American Mathematical Society ; number 1382
Abstract	"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"-- Provided by publisher.
Bibliography note	Includes bibliographical references (page 117-121) and index.
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2022048388
ISBN	9781470454333 (paperback)
ISBN	(epub)

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Hypergeometric functions over finite fields / Jenny Fuselier, Ling Long, Ravi Ramakrishna, Holly Swisher, Fang-Ting Tu.

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