Local conditions for global representations of quadratic forms

TL;DR

This paper extends the theorem of Ellenberg and Venkatesh by demonstrating that their results on representing integral quadratic forms hold under less restrictive local conditions, broadening the theorem's applicability.

Contribution

It introduces weaker local conditions for the representation of quadratic forms, improving upon previous theorems by Ellenberg and Venkatesh.

Findings

Representation theorem holds under weaker local conditions

Broader class of quadratic forms can be represented

Enhanced understanding of local-global principles in quadratic forms

Abstract

We show that the theorem of Ellenberg and Venkatesh on representation of integral quadratic forms by integral positive definite quadratic forms is valid under weaker conditions on the represented form.