Displaying similar documents to “Sums of coefficients of Hecke series”

On sums of Hecke series in short intervals

Aleksandar Ivić (2001)

Journal de théorie des nombres de Bordeaux

Similarity:

We have ∑ K - G ≤ k j ≤ K + G α j H j 3 ( 1 2 ) ≪ ϵ G K 1 + ϵ for K ϵ ≤ G ≤ K , where α j = ρ j ( 1 ) 2 ( cosh π k j ) - 1 , and ρ j ( 1 ) is the first Fourier coefficient of the Maass wave form corresponding to the eigenvalue λ j = k j 2 + 1 4 to which the Hecke series H j ( s ) is attached. This result yields the new bound H j ( 1 2 ≪ ϵ k j 1 3 + ϵ .

Three two-dimensional Weyl steps in the circle problem II. The logarithmic Riesz mean for a class of arithmetic functions

Ulrike M. A. Vorhauer (1999)

Acta Arithmetica

Similarity:

1. Summary. In Part II we study arithmetic functions whose Dirichlet series satisfy a rather general type of functional equation. For the logarithmic Riesz mean of these functions we give a representation involving finite trigonometric sums. An essential tool here is the saddle point method. Estimation of the exponential sums in the special case of the circle problem will be the topic of Part III.