A proof of the S-genus identities for ternary quadratic forms
Number Theory
2011-04-14 v2
Abstract
In this paper we prove the main conjectures of Berkovich and Jagy about weighted averages of representation numbers over an S-genus of ternary lattices (defined below) for any odd squarefree S \in N. We do this by reformulating them in terms of local quantities using the Siegel-Weil and Conway-Sloane formulas, and then proving the necessary local identities. We conclude by conjecturing generalized formulas valid over certain totally real number fields as a direction for future work.
Keywords
Cite
@article{arxiv.1010.1926,
title = {A proof of the S-genus identities for ternary quadratic forms},
author = {Alexander Berkovich and Jonathan Hanke and William Jagy},
journal= {arXiv preprint arXiv:1010.1926},
year = {2011}
}
Comments
14 pages