Trigonometric Selector Kernels, Duality, and Odd Zeta Values
General Mathematics
2025-09-16 v1
Abstract
In this short note, we develop trigonometric selector kernels to represent odd zeta values via dual hyperbolic counterparts. This framework highlights a Fourier-Poisson duality, incorporating finite-part integrals in the sense of Hadamard-Galapon. In particular, we show how such kernels naturally recover Euler-Maclaurin and Poisson summation formulas as dual manifestations. We further connect our kernel approach with the finite-part integral formulation, extending earlier Cvijovi\'c-Klinowski type representations for odd zeta values.
Cite
@article{arxiv.2509.10801,
title = {Trigonometric Selector Kernels, Duality, and Odd Zeta Values},
author = {Ken Nagai},
journal= {arXiv preprint arXiv:2509.10801},
year = {2025}
}