Geodesic
Fourier coefficients of theta functions at cusps other than infinity
Joseph Hundley 1   ; Qiao Zhang 2
1 Department of Mathematics University at Buffalo 244 Mathematics Building Buffalo, NY 14260-2900, U.S.A.
2 Department of Mathematics Texas Christian University Fort Worth, TX 76129, U.S.A.
Acta Arithmetica, Tome 175 (2016) no. 4, pp. 341-383 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/aa8278-4-2016
Keywords: consider theta functions twisted certain dirichlet characters derive explicit formulae their fourier coefficients cusps other infinity method based expressing these theta functions terms explicit elements adelic schwartz space studying action adelic metaplectic group formulae obtained quite amenable effective computations contrast those available previous work goldfeld hundley lee integral weight particular prove conjecture goldfeld gunnells twisted theta functions

Joseph Hundley  1   ; Qiao Zhang  2

1 Department of Mathematics University at Buffalo 244 Mathematics Building Buffalo, NY 14260-2900, U.S.A.
2 Department of Mathematics Texas Christian University Fort Worth, TX 76129, U.S.A. 
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Joseph Hundley; Qiao Zhang. Fourier coefficients of theta functions at cusps other than infinity. Acta Arithmetica, Tome 175 (2016) no. 4, pp. 341-383. doi: 10.4064/aa8278-4-2016

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