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

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

2010-10-10

arxiv.org/abs/1010.1926v2

Mathematics

Number Theory

14 pages

Scientific paper

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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