CM periods, CM regulators and hypergeometric functions, II

TL;DR

This paper investigates periods and regulators of specific algebraic fibrations with multiplication by a number field, expressing them through hypergeometric functions and gamma values, supporting the Gross-Deligne conjecture.

Contribution

It provides explicit formulas for periods and regulators in terms of hypergeometric functions and gamma values, advancing understanding of their relation to the Gross-Deligne conjecture.

Findings

Periods expressed via hypergeometric functions and gamma values

Supports the Gross-Deligne conjecture with explicit examples

Advances the computation of regulators in algebraic geometry

Abstract

We study periods and regulators of a certain class of fibrations of varieties whose relative $H^1$ has multiplication by a number field. Both are written in terms of values of hypergeometric functions ${}_3F_2$ and the former reduces to values of the gamma function, which provide examples of the conjecture of Gross-Deligne.