Average behavior of Fourier coefficients of Maass cusp forms for hyperbolic -manifolds

作者：Jiang, Yujiao^*; Lu, Guangshi

来源：Monatshefte fur Mathematik, 2015, 178(2): 221-236.

DOI：10.1007/s00605-015-0766-z

• Fourier coefficients
• Maass cusp forms
• Hyperbolic 3-manifolds

Let lambda(phi)(n) be the n-th Fourier coefficient of a doubly even and normalized Hecke-Maass cusp form for hyperbolic 3-manifolds. In this paper, we investigate the behavior of summatory functions in the following
(i) the j-th power sum of lambda(phi)(n)
Sigma(N(n)<= x)lambda(phi)(n)(j),
where j <= 8;
(ii) the sum of lambda(phi)(n) over the sparse sequence n(l)
Sigma(N(n)<= x)lambda(phi)(n)(l),
where l <= 4;
(iii) the hybrid sum for lambda(phi)(n)
Sigma(N(n)<= x)lambda(phi)(n(l))(j),
where 2 <= l <= 4, j = 2, or l = 2, j = 4.

• 出版日期2015-10
• 单位山东大学