Certain transformations and values of p-adic hypergeometric functions

Let p be an odd prime and [Formula: see text], [Formula: see text]. For positive integers n, let [Formula: see text] denote McCarthy’s p-adic hypergeometric function. In this paper, we prove an identity expressing a [Formula: see text] hypergeometric function as a sum of two [Formula: see text] hypergeometric functions. This identity generalizes some known identities satisfied by the finite field hypergeometric functions. We also prove a transformation that relates [Formula: see text] and [Formula: see text] hypergeometric functions. Next, we express the trace of Frobenius of elliptic curves in terms of special values of [Formula: see text] and [Formula: see text] hypergeometric functions. Our results extend the recent works of Tripathi and Meher on the finite field hypergeometric functions to wider classes of primes.

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Certain transformations and values of p-adic hypergeometric functions

Cited by 2 publications

References 30 publications

Diagonal hypersurfaces and elliptic curves over finite fields and hypergeometric functions

Diagonal hypersurfaces and elliptic curves over finite fields and hypergeometric functions

p-Adic hypergeometric functions and the trace of Frobenius of elliptic curves

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