Counting and zeta functions over F1
Number Theory
2017-09-04 v2
Abstract
A new interpretation of zeta functions is given for F1-schemes which do not satisfy Soul\'e's condition. Functional equations for reductive groups are computed and a new definition of zeta functions attached to more general counting functions is given which is based on regularization and puts on an equal footing F1-theory on the one hand and spectral theory of Laplace operators on manifolds on the other.
Cite
@article{arxiv.1306.3681,
title = {Counting and zeta functions over F1},
author = {Anton Deitmar and Shin-Ya Koyama and Nobushige Kurokawa},
journal= {arXiv preprint arXiv:1306.3681},
year = {2017}
}