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Kane, Ben; Kim, Daejun; Varadharajan, Srimathi
Transactions of the American Mathematical Society, March 1, 2023, 2023-3-00, Letnik: 376, Številka: 3Journal Article
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.
