On special values of generalized $p$-adic hypergeometric functions of logarithmic type

Yusuke Nemoto

On special values of generalized $p$-adic hypergeometric functions of logarithmic type

Number Theory 2026-05-07 v2 Algebraic Geometry

Authors: Yusuke Nemoto

Abstract

We introduce a new type of $p$ -adic hypergeometric functions, which are generalizations of $p$ -adic hypergeometric functions of logarithmic type defined by Asakura, and show that these functions satisfy the congruence relations similar to Asakura's. We also give numerical computations of the special values of these functions at $t=1$ and prove that these values are equal to zero under some conditions.

Keywords

$p$-adic hypergeometric functions logarithmic type special values congruence relations numerical computation

Cite

@article{arxiv.2509.07895,
  title  = {On special values of generalized $p$-adic hypergeometric functions of logarithmic type},
  author = {Yusuke Nemoto},
  journal= {arXiv preprint arXiv:2509.07895},
  year   = {2026}
}

Comments

22 pages, 1 figure

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