Oscillations of Fourier coefficients of cusp forms over primes

作者：Hou, Fei^*; Lu, Guangshi

来源：Journal of Number Theory, 2016, 159: 370-383.

DOI：10.1016/j.jnt.2015.07.007

• Exponential sums
• Fourier coefficient
• Cusp form

Let f be a primitive holomorphic or Maass cusp form for the group SL(2,Z), and a(f)(n) its nth normalized Fourier coefficient. It is proved that, for any alpha,beta is an element of R, there exists an effective positive constant c such that
Sigma(n <= N) Lambda(n)a(f()n)e(alpha n(2) + beta n) <<(f) N exp(-c root log N).

• 出版日期2016-2
• 单位山东大学