Fourier coefficients of theta functions at cusps other than infinity
Acta Arithmetica, Tome 175 (2016) no. 4, pp. 341-383
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
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
Affiliations des auteurs :
Joseph Hundley 1 ; Qiao Zhang 2
@article{10_4064_aa8278_4_2016,
author = {Joseph Hundley and Qiao Zhang},
title = {Fourier coefficients of theta functions at cusps other than infinity},
journal = {Acta Arithmetica},
pages = {341--383},
publisher = {mathdoc},
volume = {175},
number = {4},
year = {2016},
doi = {10.4064/aa8278-4-2016},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/aa8278-4-2016/}
}
TY - JOUR AU - Joseph Hundley AU - Qiao Zhang TI - Fourier coefficients of theta functions at cusps other than infinity JO - Acta Arithmetica PY - 2016 SP - 341 EP - 383 VL - 175 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/aa8278-4-2016/ DO - 10.4064/aa8278-4-2016 LA - en ID - 10_4064_aa8278_4_2016 ER -
%0 Journal Article %A Joseph Hundley %A Qiao Zhang %T Fourier coefficients of theta functions at cusps other than infinity %J Acta Arithmetica %D 2016 %P 341-383 %V 175 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/aa8278-4-2016/ %R 10.4064/aa8278-4-2016 %G en %F 10_4064_aa8278_4_2016
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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