Oscillations of cusp form coefficients in exponential sums

作者：Pi Qinghua^*; Sun Qingfeng

来源：Ramanujan Journal, 2010, 21(1): 53-64.

DOI：10.1007/s11139-008-9151-z

• Fourier coefficients of cusp forms
• Exponential sums

Let f (z) = Sigma n(infinity)=1 lambda(n)n((k-1)/2)e(nz) be a holomorphic cusp form of weight. for the full modular group SL(2)(Z) and let mu(n) be the Mobius function. In this paper, we are concerned with the sum
S(alpha, X) = Sigma n <= X mu(n)lambda(n)e(alpha root n), 0 not equal alpha is an element of R.
It is proved that, unconditionally, S(alpha, X) << X(5/6) (logX)(20), where the implied constant depends only on a and the cusp form f.

• 出版日期2010-1
• 单位山东大学