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

作者：Zhou Fan^*

来源：Ramanujan Journal, 2014, 35(3): 405-425.

DOI：10.1007/s11139-013-9535-6

• Maass form
• Automorphic form
• Kuznetsov trace formula
• Sato-Tate measure
• Sato-Tate conjecture
• Satake parameter
• Casselman-Shalika formula
• Equidistribution
• Ramanujan conjecture
• Orthogonality relation
• Trace formula

We formulate a conjectured orthogonality relation between the Fourier coefficients of Maass forms on PGL(N). Based on the works of Goldfeld-Kontorovich and Blomer for N=3, and on our conjecture for Na parts per thousand yen4, 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.

• 出版日期2014-12