Explicit class number formulas for Siegel–Weil averages of ternary quadratic forms

Kane, Ben; Kim, Daejun; Varadharajan, Srimathi

doi:10.1090/tran/8814

Explicit class number formulas for Siegel–Weil averages of ternary quadratic forms
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by Ben Kane, Daejun Kim and Srimathi Varadharajan HTML | PDF

Trans. Amer. Math. Soc. 376 (2023), 1625-1652 Request permission

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 lattice 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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