Near-miss Identities and Spinor Genus Classification of Ternary Quadratic Forms with Congruence Conditions

TL;DR

This paper establishes near-miss identities for counting representations of certain ternary quadratic forms with congruence conditions, classifies their genus and spinor genus, and provides a comprehensive classification for specific lattice cosets.

Contribution

It introduces new near-miss identities and offers a complete classification of genus and spinor genus for conductor 2 lattice cosets of 2-adically unimodular lattices.

Findings

Derived near-miss identities for specific quadratic forms

Classified genus and spinor genus of related lattice cosets

Provided a complete classification for conductor 2 lattice cosets

Abstract

In this paper, near-miss identities for the number of representations of some integral ternary quadratic forms with congruence conditions are found and proven. The genus and spinor genus of the corresponding lattice cosets are then classified. Finally, a complete genus and spinor genus classification for all conductor 2 lattice cosets of 2-adically unimodular lattices is given.