A proof of the S-genus identities for ternary quadratic forms

Alexander Berkovich; Jonathan Hanke; William Jagy

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arXiv · 1010.1926

A proof of the S-genus identities for ternary quadratic forms

Alexander Berkovich·Jonathan Hanke·William Jagy

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Abstract

In this paper we prove the main conjectures of Berkovich and Jagy about weighted averages of representation numbers over an S-genus of ternary lattices (defined below) for any odd squarefree S \in N. We do this by reformulating them in terms of local quantities using the Siegel-Weil and Conway-Sloane formulas, and then proving the necessary local identities. We conclude by conjecturing generalized formulas valid over certain totally real number fields as a direction for future work.

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BibTeX RIS

Alexander Berkovich, Jonathan Hanke, William Jagy. 2010-10-10. A proof of the S-genus identities for ternary quadratic forms. https://arxiv.org/abs/1010.1926

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