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arXiv · 1609.06563

Quadratic forms representing all integers coprime to 3

Justin DeBenedetto·Jeremy Rouse
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Abstract

Following Bhargava and Hanke's celebrated 290-theorem, we prove a universality theorem for all positive-definite integer-valued quadratic forms that represent all positive integers coprime to $3$. In particular, if a positive-definite quadratic form represents all positive integers coprime to $3$ and $\leq 290$, then it represents all positive integers coprime to $3$. We use similar methods to those used by Rouse to prove (assuming GRH) that a positive-definite quadratic form representing every odd integer between $1$ and $451$ represents all positive odd integers.

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Justin DeBenedetto, Jeremy Rouse. 2016-09-21. Quadratic forms representing all integers coprime to 3. https://arxiv.org/abs/1609.06563

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