SPHERICAL FUNCTIONS FOR GLn OVER LOCAL FIELDS, AND SUMMATION OF HECKE SERIES
SPHERICAL FUNCTIONS FOR GLn OVER LOCAL FIELDS, AND SUMMATION OF HECKE SERIES
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局部场上 GLn 的球函数以及 Hecke 级数的求和
DOI：
10.1070/sm1970v012n03abeh000929
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发表时间：
1970
期刊：
影响因子：
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通讯作者：
A. Andrianov
中科院分区：
文献类型：
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作者：
A. Andrianov
在？？给出了群GLn（D）上带状球函数的1和2个显式公式.这里D是具有有限剩余类域的离散赋范域上的有限秩除代数。在哪？3这些公式被应用于群GLn（D）上的多重Hecke级数和n元zeta函数的求和。在哪？4、结果？3应用于局部域上亏格为n的辛群上的Hecke级数和Zeta函数的求和。证明了佐竹关于zeta函数的分母形式的猜想和志村关于分子和分母的次数的猜想。参考书目：7项。
In ?? 1 and 2 explicit formulas for zonal spherical functions on the group GLn(D) are derived. Here D is a division algebra of finite rank over a discrete normed field with finite residue class field. In ? 3 these formulas are applied to summation of multiple Hecke series and zeta-functions in n variables on the group GLn(D). In ? 4 the results of ? 3 are applied to summation of Hecke series and zeta-functions on the symplectic group of genus n over local fields. Furthermore, the following conjectures are proved: the conjecture of Satake about the form of the denominator of zeta-functions, and the conjecture of Shimura about the degrees of the numerator and the denominator. Bibliography: 7 items.