On the regulator of Fermat motives and generalized hypergeometric functions

TL;DR

This paper computes Beilinson regulators for Fermat curve motives, expressing them via hypergeometric functions, and provides evidence supporting the Beilinson conjecture on L-function special values.

Contribution

It introduces explicit calculations of regulators linked to Fermat motives using hypergeometric functions, advancing understanding of Beilinson's conjecture.

Findings

Regulators are expressed through special hypergeometric values.

Results support the surjectivity of regulators as predicted by Beilinson.

Provides new evidence for the Beilinson conjecture on L-functions.

Abstract

We calculate the Beilinson regulators of motives associated to Fermat curves and express them by special values of generalized hypergeometric functions. As a result, we obtain surjectivity results of the regulator, which support the Beilinson conjecture on special values of L-functions.