On The Gauss EYPHKA Theorem And Some Allied Inequalities

preprint2014arXivOpen access

Abstract

We use the 1907 Hurwitz formula along with the Jacobi triple product identity to understand representation properties of two JP (Jones-Pall) forms of Kaplansky: 9x^2+ 16y^2 +36z^2 + 16yz+ 4xz + 8xy and 9x^2+ 17y^2 +32z^2 -8yz+ 8xz + 6xy. We also discuss three nontrivial analogues of the Gauss EYPHKA theorem. The technique used can be applied to all known spinor regular ternary quadratic forms.

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