Quaternary quadratic forms with prime discriminant

Jeremy Rouse; Katherine Thompson

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arXiv · 2206.00412

Quaternary quadratic forms with prime discriminant

Jeremy Rouse·Katherine Thompson

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Abstract

Let $Q$ be a positive-definite quaternary quadratic form with prime discriminant. We give an explicit lower bound on the number of representations of a positive integer $n$ by $Q$. This problem is connected with deriving an upper bound on the Petersson norm $\langle C, C \rangle$ of the cuspidal part of the theta series of $Q$. We derive an upper bound on $\langle C, C \rangle$ that depends on the smallest positive integer not represented by the dual form $Q^{*}$. In addition, we give a non-trivial upper bound on the sum of the integers $n$ excepted by $Q$.

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BibTeX RIS

Jeremy Rouse, Katherine Thompson. 2022-06-01. Quaternary quadratic forms with prime discriminant. https://arxiv.org/abs/2206.00412

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