Summation identities and special values of hypergeometric series in the p-adic setting

2014/08/21 by Rupam Barman, Barman, Rupam, Neelam Saikia +3
Mathematics · #11S80 #11T24 #33E50 #FOS: Mathematics #Number Theory (math.NT) #Primary: 11G20 #Secondary: 33C99 #math.NT #msc:11G20 #msc:11S80 #msc:11T24 #msc:33C99 #msc:33E50

paper · pdf · doi:10.48550/arxiv.1408.5003

27 pages

arxiv created 2014/08/21 · arxiv updated 2014/08/22

Abstract

We prove hypergeometric type summation identities for a function defined in terms of quotients of the p-adic gamma function by counting points on certain families of hyperelliptic curves over \mathbbF_q. We also find certain special values of that function.

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• Summation identities and transformations for hypergeometric series
• Certain Transformations for Hypergeometric series in p-adic setting
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