Fourier coefficients of theta functions at cusps other than infinity

Volume 175 / 2016

Joseph Hundley, Qiao Zhang Acta Arithmetica 175 (2016), 341-383 MSC: Primary 11F27; Secondary 11F30. DOI: 10.4064/aa8278-4-2016 Published online: 5 October 2016


We consider theta functions twisted by certain Dirichlet characters, and derive explicit formulae for their Fourier coefficients at cusps other than infinity. The method is based on expressing these theta functions in terms of explicit elements of the adelic Schwartz space and studying the action of the adelic metaplectic group on them. The formulae obtained are quite amenable to effective computations, in contrast to those available in the previous work of Goldfeld, Hundley and Lee on the integral weight case. In particular, we prove a conjecture of Goldfeld and Gunnells on twisted theta functions.


  • Joseph HundleyDepartment of Mathematics
    University at Buffalo
    244 Mathematics Building
    Buffalo, NY 14260-2900, U.S.A.
  • Qiao ZhangDepartment of Mathematics
    Texas Christian University
    Fort Worth, TX 76129, U.S.A.

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