UNIFORM ESTIMATES FOR SUMS OF FOURIER COEFFICIENTS OF CUSP FORMS

作者：Lue G S

来源：Acta Mathematica Hungarica, 2009, 124(1-2): 83-97.

DOI：10.1007/s10474-009-8153-7

• Fourier coefficient of cusp forms
• symmetric square L-function
• Rankin-Selberg L-function

Let k be an even positive integer and f a holomorphic Hecke eigenform of weight k with respect to the full modular group SL(2,Z). Let c(n) be the nth coefficient of the symmertic square L-function associated to f. We study the uniform bound for the sum C(x) = Sigma(n <= x) c(n) with respect to the weight k and establish that
C(x) = Sigma(n <= x) c(n) << x(5/3)(log x)(22/5) k(3/2)(log x)(5).
Other similar results are also established.

• 出版日期2009-7
• 单位山东大学