Alexander Berkovich, Jonathan Hanke, William Jagy
Published 2010-10-10, updated 2011-04-13Version 2
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.
On representation of an integer as a sum by X^2+Y^2+Z^2 and the modular equations of degree 3 and 5
Sums of squares in $S$-integers
A generalization of Watson transformation and representations of ternary quadratic forms
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