Strong q-analogues for values of the Dirichlet beta function

Authors

Ankush Goswami, The University of Texas Rio Grande Valley
Tim Huber, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

2026

Abstract

An infinite class of relations between modular forms is constructed that generalizes evaluations of the Dirichlet beta function at odd positive integers. The work is motivated by a base case appearing in Ramanujan’s Notebooks and a parallel construction for the Riemann zeta function. The identities are shown to be strong q-analogues by virtue of their reduction to the classical beta evaluations as 𝑞→1− and explicit evaluations at CM points for |𝑞|< 1. We also determine asymptotic formulas for the Fourier coefficients of the associated modular forms.

Comments

Original published version available at https://doi.org/10.1142/S1793042126500363

Recommended Citation

Goswami, Ankush, and Timothy Huber. 2026. “Strong Q-Analogues for Values of the Dirichlet Beta Function.” International Journal of Number Theory 22 (03): 677–95. https://doi.org/10.1142/S1793042126500363.

Publication Title

International Journal of Number Theory

DOI

10.1142/S1793042126500363