On certain analogues of Eisenstein series and their evaluation formulas of Hurwitz type
On certain analogues of Eisenstein series and their evaluation formulas of Hurwitz type
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DOI：
10.1112/blms/bdn014
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发表时间：
2008-04-01
影响因子：
0.9
通讯作者：
Tsumura, Hirofumi
中科院分区：
文献类型：
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作者：
Tsumura, Hirofumi
在这篇文章中，我们考虑了包含双曲正弦和余弦函数的某些Eisenstein级数的类似。利用Hurwitz的一个结果，我们证明了这些级数在正整数处的一些求值公式。我们可以把这些公式看作是柯西、Ramanujan、Berndt等人给出的某些级数的著名公式以及Hurwitz给出的Eisenstein级数的公式的类似。
In this paper, we consider certain analogues of Eisenstein series involving hyperbolic sine and cosine functions. Using a result of Hurwitz, we prove some evaluation formulas for these series at positive integers. We can regard these formulas as analogues of the famous formulas for certain series given by Cauchy, Ramanujan, Berndt, and so on, as well as those for the Eisenstein series given by Hurwitz.