Rationality of secant zeta values

TL;DR

This paper proves a conjecture about the algebraic properties of special values of secant zeta functions using generalized eta-functions, advancing understanding in number theory.

Contribution

It introduces a novel application of Arakawa-Berndt theory to establish algebraic nature of secant zeta values, resolving a conjecture in the field.

Findings

Proved the algebraic nature of secant zeta values at specific points.

Connected generalized eta-functions with secant zeta function values.

Confirmed a conjecture by Lal ext{in}, Rodrigue, and Rogers.

Abstract

We use the Arakawa-Berndt theory of generalized eta-functions to prove a conjecture of Lal\`in, Rodrigue and Rogers concerning the algebraic nature of special values of the secant zeta functions.