Trigonometric Selector Kernels, Duality, and Odd Zeta Values

2025/09/13 by Ken Nagai, Nagai, Ken · 2 citations
Mathematics · #Advanced Mathematical Identities #Approximation Theory and Sequence Spaces #FOS: Mathematics #General Mathematics (math.GM) #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2509.10801

openalex publication_date 2025/09/13 · openalex created_date 2025/10/12 · openalex updated_date 2026/07/28

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 Cvijović-Klinowski type representations for odd zeta values.

Cited by

• Dual Bases for Analytic Bernoulli Functions
• Analytic Bernoulli Functions: Correspondence with Hermite Polynomials

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