On the algebraic independence of periods of abelian varieties and their exponentials

TL;DR

This paper extends a known result on the algebraic independence of abelian variety periods to include their exponentials, with applications to beta function values at rational points.

Contribution

It generalizes Vasil'ev's result to cases involving exponentials of periods, providing new insights into algebraic independence and special function values.

Findings

Extended algebraic independence results to exponentials of periods.

Derived applications to beta function values at rational points.

Enhanced understanding of the interplay between periods and their exponentials.

Abstract

We generalize a result by Vasil'ev on the algebraic independence of periods of abelian varieties to the case when some of these periods are replaced by their exponentials. We eventually derive some applications to values of the beta function at rational points.