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arXiv · 1303.0889

Weighted Sato-Tate Vertical Distribution of the Satake Parameter of Maass Forms on PGL(N)

Fan Zhou
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Abstract

We formulate a conjectured orthogonality relation between the Fourier coefficients of Maass forms on PGL(N) for N>=2. Based on the work of Goldfeld-Kontorovich and Blomer for N=3, and on our conjecture for N>=4, we prove a weighted vertical equidistribution theorem (with respect to the generalized Sato-Tate measure) for the Satake parameter of Maass forms at a finite prime. For N=3, the rate of convergence for the equidistribution theorem is obtained.

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BibTeXRIS

Fan Zhou. 2013-08-01. Weighted Sato-Tate Vertical Distribution of the Satake Parameter of Maass Forms on PGL(N). https://doi.org/10.1007/s11139-013-9535-6

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