Open AccessTwisted Eisenstein series, cotangent‐zeta sums, and quantum modular forms
Author(s) -
Folsom Amanda
Publication year - 2020
Publication title -
transactions of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.43
H-Index - 7
ISSN - 2052-4986
DOI - 10.1112/tlm3.12022
Subject(s) - eisenstein series , series (stratigraphy) , modular form , trigonometric functions , mathematics , pure mathematics , modular design , riemann zeta function , quantum , algebra over a field , physics , quantum mechanics , geometry , computer science , paleontology , biology , operating system
Abstract We define twisted Eisenstein seriesE s ± ( 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 ofC ′ : = 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 .