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Fourier coefficients of sextic theta series


Authors: Reinier Bröker and Jeff Hoffstein
Journal: Math. Comp. 85 (2016), 1901-1927
MSC (2010): Primary 11Y35
DOI: https://doi.org/10.1090/mcom3044
Published electronically: October 21, 2015
MathSciNet review: 3471113
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Abstract: This article focuses on the theta series on the 6-fold cover of $ \mathrm {GL}_2$. We investigate the Fourier coefficients $ \tau (r)$ of the theta series, and give partially proven, partially conjectured values for $ \tau (\pi )^2$, $ \tau (\pi ^2)$ and $ \tau (\pi ^4)$ for prime values $ \pi $.


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Additional Information

Reinier Bröker
Affiliation: Brown University, Department of Mathematics, Box 1917, Providence, Rhode Island
Email: reinier@math.brown.edu

Jeff Hoffstein
Affiliation: Brown University, Department of Mathematics, Box 1917, Providence, Rhode Island
Email: jhoff@math.brown.edu

DOI: https://doi.org/10.1090/mcom3044
Received by editor(s): February 21, 2014
Received by editor(s) in revised form: October 18, 2014, and January 21, 2015
Published electronically: October 21, 2015
Article copyright: © Copyright 2015 American Mathematical Society