摘要
Let f be a holomorphic cusp form of weight k for SL2(Z) and λf(n) its n-th Fourier coefficient.In this paper,the exponential sum X【n 2X λf(n)e(αnβ) twisted by Fourier coefficients λf(n) is proved toh ave a main term of size |λf(q)|X3/4 when β = 1/2 and α is close to ±2√q,q ∈ Z,and is smaller otherwise for β 【 3/4.This is a manifestation of the resonance spectrum of automorphic forms for SL2(Z).
Let f be a holomorphic cusp form of weight k for SL2(Z) and λf(n) its n-th Fourier coefficient.In this paper,the exponential sum X<n 2X λf(n)e(αnβ) twisted by Fourier coefficients λf(n) is proved toh ave a main term of size |λf(q)|X3/4 when β = 1/2 and α is close to ±2√q,q ∈ Z,and is smaller otherwise for β < 3/4.This is a manifestation of the resonance spectrum of automorphic forms for SL2(Z).
基金
supported in part by National Basic Research Program of China (973-Program) (Grant No.)
National Natural Science Foundation of China (Grant No.10971119)
