Summation and the Poisson formula
Number Theory
2020-02-11 v3 Functional Analysis
Abstract
By giving the definition of the sum of a series indexed by a set on which a group acts, we prove that the sum of the series that defines the Riemann zeta function, the Epstein zeta function, and a few other series indexed by has an intrinsic meaning as a complex number, independent of the requirements of analytic continuation. The definition of the sum requires nothing more than algebra and the concept of absolute convergence. The analytical significance of the algebraically defined sum is then explained by an argument that relies on the Poisson formula for tempered distributions.
Cite
@article{arxiv.1204.3533,
title = {Summation and the Poisson formula},
author = {Madhav V. Nori},
journal= {arXiv preprint arXiv:1204.3533},
year = {2020}
}
Comments
Several recommendationsof the reviewer to improve readability of the paper have been adopted