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Barman, Rupam; Saikia, Neelam

Certain transformations for hypergeometric series in the \(p\)-adic setting. (English) Zbl 1365.11121

Int. J. Number Theory 11, No. 2, 645-660 (2015).
Summary: In [Pac. J. Math. 261, No. 1, 219–236 (2013; Zbl 1296.11079)], D. McCarthy defined a function \(_nG_n[\cdots]\) using the Teichmüller character of finite fields and quotients of the \(p\)-adic gamma function. This function extends hypergeometric functions over finite fields to the \(p\)-adic setting. In this paper, we give certain transformation formulas for the function \(_nG_n[\cdots]\) which are not implied from the analogous hypergeometric functions over finite fields.

Cited in 8 Documents

MSC:

11S80 Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)
33E50 Special functions in characteristic \(p\) (gamma functions, etc.)
11T24 Other character sums and Gauss sums
11G20 Curves over finite and local fields

Keywords:

character of finite fields; Gaussian hypergeometric series; elliptic curves; trace of Frobenius; Teichmüller character; \(p\)-adic gamma function

Citations:

Zbl 1296.11079
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Full Text: DOI arXiv

References:

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