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

2020/03/24 by Asakura, Masanori · 2 citations
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2003.10652

Abstract

The Ross symbol is defined to be an element 1-z,1-w\ in K₂ of a Fermat curve zⁿ+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-x₀^n₀)⋯(1-x_d^n_d)=t. The main result is that the Beilinson regulator is described by the hypergeometric functions _d+3F_d+2's.

Cited by

• On special values of generalized p-adic hypergeometric functions of logarithmic type
• Transformation formula of Dwork's p-adic hypergeometric function

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