On the conical zeta values and the Dedekind zeta values for totally real fields
On the conical zeta values and the Dedekind zeta values for totally real fields
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发表时间：
2022-11
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通讯作者：
Hohto Bekki
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作者：
Hohto Bekki
。锥形zeta值是凸锥上多个zeta值的推广，它们由一定的倍数和去fiNed。本文给出了全实fi域上Dedekindzeta函数的值与某些代数锥上的锥zeta值之间的关系。更确切地说，我们证明了全实fi域的部分zeta函数的值可以表示为与某些代数锥相关的锥zeta值的有理线性组合，直到判别式的平方根。
. The conical zeta values are a generalization of the multiple zeta values which are defined by certain multiple sums over convex cones. In this paper, we present a relation between the values of the Dedekind zeta functions for totally real fields and the conical zeta values for certain algebraic cones. More precisely, we show that the values of the partial zeta functions for totally real fields can be expressed as a rational linear combination of the conical zeta values associated with certain algebraic cones up to the square root of the discriminant.