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 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 dc:creator

• Zhou, Fan

• Mathematics
• Automorphic forms
• Eigenvalues
• Fourier series

Language dc:language

English

DOI dc:identifier

https://doi.org/10.7916/D8DR32QQ

OAI identifier oai:identifier

oai:academiccommons.columbia.edu:10.7916/D8DR32QQ