ON THE ANALYTIC PROPERTIES OF STANDARD ZETA FUNCTIONS OF SIEGEL MODULAR FORMS
ON THE ANALYTIC PROPERTIES OF STANDARD ZETA FUNCTIONS OF SIEGEL MODULAR FORMS
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西格尔模形式标准ZETA函数的解析性质
DOI：
10.1070/sm1979v035n01abeh001443
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发表时间：
1979
期刊：
影响因子：
--
通讯作者：
V. Kalinin
中科院分区：
文献类型：
--
作者：
A. Andrianov;V. Kalinin
证明了关于任意偶次Siegel模群的形式同余子群的全纯尖点形式的标准Zeta函数(类似于Rankin和Shimura的Zeta函数)具有亚纯连续.对于这种情况，在附加一些限制条件下，证明了Zeta函数除了有限个极点外是全纯的，并得到了一个函数方程。参考书目：9个标题。
It is proved that standard zeta functions (analogs of the zeta functions of Rankin and Shimura) for holomorphic cusp forms with respect to congruence subgroups of the form of the Siegel modular group of arbitrary even degree have a meromorphic continuation. For the case , with some additional restrictions, it is proved that the zeta functions are holomorphic except for a finite number of poles, and a functional equation is obtained.Bibliography: 9 titles.