On a sum involving Fourier coefficients of cusp forms

Ω-Result on Coefficients of Automorphic L-Functions Over Sparse Sequences

“…Denoting by ∆ j (f ; x) the error term in (1.3), they also obtained the lower bound of ∆ j (f ; x) using the Omega Theorem of Kühleitner and Nowak [9]. On the other hand, the sum over squares n≤x λ f (n 2 ) was considered in Ivić [5], Fomenko [2] and Sankaranarayanan [20]. Lü [14] obtained the bound of n≤x λ f (n j ) (j = 3, 4).…”

On Riesz means of the coefficients of spinor zeta functions in genus two

“…As in Lemma 3.4 of [9], we apply the maximum-modulus principle (see Theorem 5.53 in [6]) to the function F (w) = Z F (s)e (w−s) 2 X w−s in the rectangle with vertex points…”

Uniform estimates for sums of Fourier coefficients of cusp forms

“…The rst aim of this paper is to establish uniform results for C(x) with respect to the weight k. We shall show the following two results. In addition, in fact a rather minor change enables us to improve slightly the exponent of x of Sankaranarayanan's result for the sum S(x) in [12]. Theorem 1.3.…”

“…Recently Sankaranarayanan [12] established a uniform bound for S(x) with respect to the weight k. More precisely he showed that…”

“…On using (2.4), (2.5) and the PhragmenLindelöf principle, we have the following convexity bound (see for example Lemma 3.4 in [12])…”