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arXiv · 2203.16431

Explicit Class number formulas for Siegel--Weil averages of ternary quadratic forms

Ben Kane·Daejun Kim·Srimathi Varadharajan
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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 $t_j\mathbb{Z}^2$) 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.

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Ben Kane, Daejun Kim, Srimathi Varadharajan. 2022-03-30. Explicit Class number formulas for Siegel--Weil averages of ternary quadratic forms. https://arxiv.org/abs/2203.16431

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