ON THE GENERALIZED TWO VARIABLE EISENSTEIN SERIES
ON THE GENERALIZED TWO VARIABLE EISENSTEIN SERIES
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关于广义二变量爱森斯坦级数
DOI：
10.5831/hmj.2014.36.4.895
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发表时间：
2014
影响因子：
1.3
通讯作者：
Sung
中科院分区：
文献类型：
--
作者：
Sung
抽象的。本文考虑广义二元Eisenstein级数。给出了它们的解析延拓，并证明了它们的模变换公式。1.导言C. Berndt [2]给出了一类更一般的Eisenstein级数的解析延拓，并证明了它们的模变换公式。利用这些结果，他做了许多事情与adjudto变换公式和在尼特级数的身份。作者[4，5]继续他的工作，给出了一般类非全纯Eisenstein级数的解析延拓，并计算了它们的模变换公式。本文考虑广义二元Eisenstein级数。利用共轭超几何函数的性质，给出了广义二元Eisenstein级数的解析延拓。并计算了它们的模变换公式。同时超几何函数1F 1（; ;z）被定义为1F 1（; ;z）：= X1 n =0（）n（）nznn！其中（x）
Abstract. In this paper, we consider generalized two variable Eisen-stein series. We give analytic continuation and prove modular trans-formation formulae for them. 1. IntroductionB. C. Berndt [2] has given analytic continuation for a more generalclass of Eisenstein series and has proved modular transformation for-mulae for them. Using these results, he did many things with regardto transformation formulae and in nite series identities. The author[4, 5], continuing his work, gave analytic continuation for a general classof non-holomorphic Eisenstein series and computed modular transfor-mation formulae for them. In this paper, we consider generalized twovariable Eisenstein series. Applying the properties of the conuent hy-pergeometric function, we give analytic continuation for generalized twovariable Eisenstein series. And we compute the modular transformationformula for them. The conuent hypergeometric function 1 F 1 ( ; ;z) isde ned to be 1 F 1 ( ; ;z) :=X 1n=0 ( ) n ( ) n z n n!;where (x)