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Moments of Gaussian hypergeometric functions over finite fields

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dc.contributor.author Pal, Ankan
dc.date.accessioned 2025-09-17T09:56:46Z
dc.date.available 2025-09-17T09:56:46Z
dc.date.issued 2023-09
dc.identifier.uri https://projecteuclid.org/journals/functiones-et-approximatio-commentarii-mathematici/volume-69/issue-1/Moments-of-Gaussian-hypergeometric-functions-over-finite-fields/10.7169/facm/2088.short
dc.identifier.uri http://dspace.bits-pilani.ac.in:8080/jspui/handle/123456789/19413
dc.description.abstract We prove explicit formulas for certain first and second moment sums of families of Gaussian hypergeometric functions n+1Fn, n≥1, over finite fields with q elements where q is an odd prime. This enables us to find an estimate for the value 6F5(1). In addition, we evaluate certain second moments of traces of the family of Clausen elliptic curves in terms of the value 3F2(−1). These formulas also allow us to express the product of certain 2F1 and n+1Fn functions in terms of finite field Appell series which generalizes current formulas for products of 2F1 functions. We finally give closed form expressions for sums of Gaussian hypergeometric functions defined using different multiplicative characters. en_US
dc.language.iso en en_US
dc.publisher Project Euclid en_US
dc.subject Mathematics en_US
dc.subject Elliptic curves en_US
dc.subject Finite fields en_US
dc.subject Hypergeometric functions en_US
dc.subject Moments en_US
dc.title Moments of Gaussian hypergeometric functions over finite fields en_US
dc.type Article en_US


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