Some Integrals of the Dedekind Eta-function

TL;DR

This paper computes specific definite integrals involving powers of the Dedekind eta-function evaluated at imaginary arguments, providing explicit values for these integrals.

Contribution

It introduces new explicit evaluations of integrals involving the Dedekind eta-function with imaginary arguments.

Findings

Provides selected explicit integral values involving the Dedekind eta-function.

Enhances understanding of the eta-function's integral properties.

Contributes to the mathematical literature on special functions and modular forms.

Abstract

This note presents selected values of definite integrals whose integrand contains a power of the Dedekind function having imaginary argument.