Analytic Eisenstein series, theta-functions, and series relations in the spirit of Ramanujan.
Analytic Eisenstein series, theta-functions, and series relations in the spirit of Ramanujan.
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DOI：
10.1515/crll.1978.303-304.332
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发表时间：
1978
期刊：
影响因子：
--
通讯作者：
B. Berndt
中科院分区：
文献类型：
--
作者：
B. Berndt
在文[6]中，作者证明了一类相当广泛的解析Eisenstein级数的变换公式。这个变换公式很容易转换成一个大类的函数，包括和推广经典的戴德金η-函数的变换公式。文[5]详细地讨论了该定理的几种特殊情况。这些特殊的转换公式先前已由Apostol，Dieter，S.伊势基角Meyer，Schoeneberg，and others.在[6]中研究的特殊情况似乎以前没有研究过。
In [6], the author proved a transformation formula for a fairly broad class of analytic Eisenstein series. This transformation formula is easily converted into a transformation formula for a large class of functions that includes and generalizes the classical Dedekind eta-function. In [5], several special cases of the theorem were worked out in detail. These particular transformation formulae had been previously established by Apostol, Dieter, S. Iseki, C. Meyer, Schoeneberg, and others. The special cases examined in [6] appear not to have been previously studied.