On the spectrum of a differential operator on a Hilbert-P\'olya space
Classical Analysis and ODEs
2024-04-19 v1
Abstract
In this paper we study the spectrum of a fundamental differential operator on a Hilbert-P\'olya space. A number is an eigenvalue of this differential operator if and only if it is a nontrivial zero of the Riemann zeta function. An explicit formula is given for the eigenfunction associated with each nontrivial zero of the zeta function. Every eigenfunction is characterized via the Poisson summation formula by a sequence of mysterious functions whose explicit formulas are given.
Keywords
Cite
@article{arxiv.2404.11902,
title = {On the spectrum of a differential operator on a Hilbert-P\'olya space},
author = {Xian-Jin Li},
journal= {arXiv preprint arXiv:2404.11902},
year = {2024}
}