Twisted Eisenstein series, cotangent‐zeta sums, and quantum modular forms

IF 1.1 Q1 MATHEMATICS Transactions of the London Mathematical Society Pub Date : 2020-09-28 DOI:10.1112/tlm3.12022
A. Folsom
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引用次数: 1

Abstract

We define twisted Eisenstein series Es±(h,k;τ) for s∈C , and show how their associated period functions, initially defined on the upper half complex plane H , have analytic continuation to all of C′:=C∖R⩽0 . We also use this result, as well as properties of various zeta functions, to show that certain cotangent‐zeta sums behave like quantum modular forms of (complex) weight s .
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扭曲的艾森斯坦级数、余切和和量子模形式
我们为s∈C定义了扭曲的艾森斯坦级数Es±(h,k;τ),并展示了它们最初在上半复平面h上定义的相关周期函数如何对所有C′:=C∖R⩽0具有解析延拓。我们还使用这个结果以及各种ζ函数的性质来证明某些余切ζ和的行为类似于(复数)权重s的量子模形式。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
1.40
自引率
0.00%
发文量
8
审稿时长
41 weeks
期刊最新文献
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