{"title":"Twisted Eisenstein series, cotangent‐zeta sums, and quantum modular forms","authors":"A. Folsom","doi":"10.1112/tlm3.12022","DOIUrl":null,"url":null,"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 .","PeriodicalId":41208,"journal":{"name":"Transactions of the London Mathematical Society","volume":" ","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2020-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1112/tlm3.12022","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions of the London Mathematical Society","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1112/tlm3.12022","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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 .