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

2010/10/10 by Alexander Berkovich, Alexander Bérkovich, Berkovich, Alexander +5 · 1 citation
Mathematics · #11E12 #11E20 #11E25 #11F27 #11F30 #11F37 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11E12 #msc:11E20 #msc:11E25 #msc:11F27 #msc:11F30 #msc:11F37

paper · pdf · doi:10.48550/arxiv.1010.1926

14 pages

openalex publication_date 2010/10/10 · arxiv created 2011/04/13 · arxiv updated 2011/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 ∈ 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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• The Structure of Masses of rank n Quadratic Lattices of varying determinant over number fields

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