Explicit Class number formulas for Siegel--Weil averages of ternary quadratic forms
Number Theory
2022-03-31 v1
Abstract
In this paper, we investigate the interplay between positive-definite integral ternary quadratic forms and class numbers. We generalize a result of Jones relating the theta function for the genus of a quadratic form to the Hurwitz class numbers, obtaining an asymptotic formula (with a main term and error term away from finitely many bad square classes ) relating the number of lattices points in a quadratic space of a given norm with a sum of class numbers related to that norm and the squarefree part of the discriminant of the quadratic form on this lattice.
Keywords
Cite
@article{arxiv.2203.16431,
title = {Explicit Class number formulas for Siegel--Weil averages of ternary quadratic forms},
author = {Ben Kane and Daejun Kim and Srimathi Varadharajan},
journal= {arXiv preprint arXiv:2203.16431},
year = {2022}
}