Sato-Tate Problem for GL(3)

Sato-Tate Problem for GL(3)

Based upon the work of Goldfeld and Kontorovich on the Kuznetsov trace formula of Maass forms for SL(3,Z), we prove a weighted vertical equidistribution theorem (with respect to the generalized Sato-Tate measure) for the p-th Hecke eigenvalue of Maass forms, with the rate of convergence. With a conj...

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Main Author: Zhou, Fan
Language:English
Published: 2013
Subjects:
Mathematics
Online Access:https://doi.org/10.7916/D8DR32QQ
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spelling ndltd-columbia.edu-oai-academiccommons.columbia.edu-10.7916-D8DR32QQ2019-05-09T15:14:01ZSato-Tate Problem for GL(3)Zhou, Fan2013ThesesMathematicsBased upon the work of Goldfeld and Kontorovich on the Kuznetsov trace formula of Maass forms for SL(3,Z), we prove a weighted vertical equidistribution theorem (with respect to the generalized Sato-Tate measure) for the p-th Hecke eigenvalue of Maass forms, with the rate of convergence. With a conjectured orthogonality relation between the Fourier coefficients of Maass forms for SL(N,Z) for N≥4, we generalize the above equidistribution theorem to N≥4.Englishhttps://doi.org/10.7916/D8DR32QQ
collection NDLTD
language English
sources NDLTD
topic Mathematics
spellingShingle Mathematics
Zhou, Fan
Sato-Tate Problem for GL(3)
description Based upon the work of Goldfeld and Kontorovich on the Kuznetsov trace formula of Maass forms for SL(3,Z), we prove a weighted vertical equidistribution theorem (with respect to the generalized Sato-Tate measure) for the p-th Hecke eigenvalue of Maass forms, with the rate of convergence. With a conjectured orthogonality relation between the Fourier coefficients of Maass forms for SL(N,Z) for N≥4, we generalize the above equidistribution theorem to N≥4.
author Zhou, Fan
author_facet Zhou, Fan
author_sort Zhou, Fan
title Sato-Tate Problem for GL(3)
title_short Sato-Tate Problem for GL(3)
title_full Sato-Tate Problem for GL(3)
title_fullStr Sato-Tate Problem for GL(3)
title_full_unstemmed Sato-Tate Problem for GL(3)
title_sort sato-tate problem for gl(3)
publishDate 2013
url https://doi.org/10.7916/D8DR32QQ
work_keys_str_mv AT zhoufan satotateproblemforgl3
_version_ 1719045434842808320

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