Shifted convolution sums of fourier coefficients with divisor functions

作者：Lu G^*

来源：Acta Mathematica Hungarica, 2015, 146(1): 86-97.

DOI：10.1007/s10474-015-0499-4

• Fourier coefficient
• cusp form
• symmetric power L-function
• Sato-Tate conjecture

Let f(z) be a primitive holomorphic cusp form of even integral weight k for the full modular group. Denote its nth normalized Fourier coefficient (Hecke eigenvalue) by lambda (f) (n). Let d(n) be the Dirichlet divisor function. In this paper, we establish that where , ( if and only if i = j), and Aj = (2j)!/(j!(j + 1)!)..

• 出版日期2015-6
• 单位山东大学