A non-commutative multiple Dirichlet power product and an application

JOURNAL OF NUMBER THEORY

卷:199

Article

Takeda, Wataru¹ 

[1] Nagoya Univ, Dept Math, Chikusa Ku, Nagoya, Aichi 4648602, Japan

关键词: Multiple Dirichlet power product;    Mobius inversion formula;    Dedekind domain;    Explicit formula;   

DOI  :  10.1016/j.jnt.2018.11.014

来源: Elsevier

【 摘 要 】

We define a multiple Dirichlet gamma-product of ideal functions as one of the generalizations of the well-known Dirichlet product of arithmetic functions. This product is not commutative but satisfies the Mobius inversion formula. As one of its applications, we give a new type of explicit formula for the number of relatively gamma-prime lattice points on a union of hyperplanes. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free