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

TitleExplicit class number formulas for Siegel–Weil averages of ternary quadratic forms
Authors
Issue Date1-Apr-2023
PublisherAmerican Mathematical Society
Citation
Transactions of the American Mathematical Society, 2023, v. 376, n. 3, p. 1625-1652 How to Cite?
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.


Persistent Identifierhttp://hdl.handle.net/10722/340886
ISSN
2023 Impact Factor: 1.2
2023 SCImago Journal Rankings: 1.581

 

DC FieldValueLanguage
dc.contributor.authorKane, Ben-
dc.contributor.authorKim, Daejun-
dc.contributor.authorVaradharajan, Srimathi-
dc.date.accessioned2024-03-11T10:48:02Z-
dc.date.available2024-03-11T10:48:02Z-
dc.date.issued2023-04-01-
dc.identifier.citationTransactions of the American Mathematical Society, 2023, v. 376, n. 3, p. 1625-1652-
dc.identifier.issn0002-9947-
dc.identifier.urihttp://hdl.handle.net/10722/340886-
dc.description.abstract<p>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.<br></p>-
dc.languageeng-
dc.publisherAmerican Mathematical Society-
dc.relation.ispartofTransactions of the American Mathematical Society-
dc.titleExplicit class number formulas for Siegel–Weil averages of ternary quadratic forms-
dc.typeArticle-
dc.identifier.volume376-
dc.identifier.issue3-
dc.identifier.spage1625-
dc.identifier.epage1652-
dc.identifier.eissn1088-6850-
dc.identifier.issnl0002-9947-

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