Functional equations for double series of Euler type with coefficients
Functional equations for double series of Euler type with coefficients
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带系数的欧拉型双级数函数方程
DOI：
10.1016/j.aim.2016.01.016
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发表时间：
2016
影响因子：
1.7
通讯作者：
YoungJu Choie and Kohji Matsumoto
中科院分区：
文献类型：
--
作者：
YoungJu Choie and Kohji Matsumoto
证明了复系数双欧拉型级数的两类函数方程。第一个是欧拉双zeta函数的函数方程的推广，在第二位作者的前一部作品中得到了证明。第二个问题更为具体，在系数为尖点形式的傅立叶系数时得到了证明，证明过程中主要利用了模关系。作为函数方程的结果，我们能够确定平凡的零因子。
We prove two types of functional equations for double series of Euler type with complex coefficients. The first one is a generalization of the functional equation for the Euler double zeta-function, proved in a former work of the second-named author. The second one is more specific, which is proved when the coefficients are Fourier coefficients of cusp forms and the modular relation is essentially used in the course of the proof. As a consequence of functional equation we are able to determine trivial zero divisors.