论文标题
Quaternary二次形式具有主要的判别
Quaternary quadratic forms with prime discriminant
论文作者
论文摘要
让$ Q $是带有主要判别的正定二次二次形式。我们对正整数$ n $的表示形式的数量（$ q $）给出了明确的下限。这个问题与在theta系列$ q $的Cuspidal部分的Petersson Norm $ \ langle c，c \ rangle $上获得上限有关。我们在$ \ langle c，c \ rangle $上得出了一个上限，该上限取决于双表格$ q^{*} $未表示的最小正整数。此外，我们对整数$ n $的总和给出了一个非平凡的上限。
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 $Q$.
