abstract:

We consider the prehomogeneous vector space of pairs of ternary quadratic forms. For the lattice of pairs of integral ternary quadratic forms and its dual lattice, there are six zeta functions associated with the the prehomogeneous vector space. We present a conjecture which states that there are simple relations among the six zeta functions. We prove that the coefficients coincide on fundamental discriminants.

中文翻译：

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关于三元二次形式对的zeta函数的一个猜想

摘要：

我们考虑了三元二次形式对的前同质向量空间。对于整数三元二次形式对的晶格及其对偶晶格，存在六个与前同矢量空间相关的zeta函数。我们提出一个猜想，指出六个zeta函数之间存在简单关系。我们证明了这些系数在基本判别式上是一致的。