A generalization of the Ross symbols in higher K-groups and hypergeometric functions I

Masanori Asakura

A generalization of the Ross symbols in higher K-groups and hypergeometric functions I

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arxiv 2003.10652 v3 pith:PU6MGXV2 submitted 2020-03-24 math.NT

Masanori Asakura This is my paper · ORCID

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The Ross symbol is defined to be an element {1-z,1-w\} in K_2 of a Fermat curve z^n+w^m=1. Ross showed that it is non-torsion by computing the Beilinson regulator. In this paper, we introduce a generalization of the Ross symbols in K_{d+1} of a variety (1-x_0^{n_0})\cdots(1-x_d^{n_d})=t. The main result is that the Beilinson regulator is described by the hypergeometric functions {}_{d+3}F_{d+2}'s.

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Transformation formula of Dwork's $p$-adic hypergeometric function
math.NT 2025-05 conditional novelty 6.0 of 10

For a in N^{-1}Z with p not dividing N and 0<a<1, Dwork's p-adic hypergeometric function satisfies F(t)=((-1)^(d+1)t)^l F(t^{-1}) for all d, with a precise sign rule when p=2.

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