Frobenius constants for families of elliptic curves

TL;DR

This paper explores Frobenius constants associated with elliptic curves, expressing them as iterated integrals of modular forms and relating some to zeta values, advancing understanding of their algebraic and geometric properties.

Contribution

It introduces a novel representation of Frobenius constants for elliptic curves as iterated integrals of modular forms and connects them to zeta values.

Findings

Frobenius constants are represented as iterated integrals of modular forms.

Some Frobenius constants are expressed in terms of zeta values.

The work links algebraic geometry, modular forms, and special values of zeta functions.

Abstract

The paper deals with a class of periods, Frobenius constants, which describe monodromy of Frobenius solutions of differential equations arising in algebraic geometry. We represent Frobenius constants related to families of elliptic curves as iterated integrals of modular forms. Using the theory of periods of modular forms, we then witness some of these constants in terms of zeta values.