Sums of Fourier Coefficients of Cusp Forms

Shifted convolution sums of fourier coefficients with divisor functions

“…The Fourier coefficients of cusp forms are interesting and mysterious objects (see e.g. [5], [17], [14]). From the theory of Hecke operators, it is well known that λ f (n) is real and satisfies the multiplicative property…”

Integral power sums of Hecke eigenvalues

“…The main idea for our improvement is an alternative expression of G (s) in Lemma 2.1 below, different from [15,16,17,13]; this expression decomposes G (s) into a product of L-functions, general and (more importantly) of lower degree ( 3). Hence we can take advantage of their (individual or averaged) subconvexity bounds (see…”

First moments of Fourier coefficients of GL(r) cusp forms

“…Later, Lau and Lü [8] generalized the above results to Maass cusp forms φ for SL (2, Z) and also to higher symmetric powers of φ, under the assumption that the higher symmetric powers are automorphic.…”

“…Now, we want to choose η 1 , η 2 > 0 to optimize the bound in (8). First we choose η 1 so that the first two terms on the right hand side of (8) are equal.…”