When Kloosterman sums meet Hecke eigenvalues

We can show that our generalized dia- magnetic inequality (5.16) [hence (1.13)] remains valid for inhomogeneous magnetic fields in the large field limit.. However, by constructing

In this paper, we use the elementary and analytic methods to study the mean value properties of the Cochrane sums weighted by two-term exponential sums, and give two exact

We use the averaged variational principle introduced in a recent article on graph spectra [10] to obtain upper bounds for sums of eigenvalues of several partial differential op-

In [13], the author proved, under some very general conditions, that short sums of `-adic trace functions over finite fields of varying center converges in law to a Gaussian

Now we let E/F be an unramified quadratic extension of local fields. We can always write it as E w rel /F v rel for a suitable quadratic extension of number fields of the

En particulier, nous obtenons une version améliorée de l’inégalité de Vaughan en appliquant une version explicite d’une inégalité dans [5] liée à la fonction de Möbius..

To control the terms around the central point d ∈ [x 1/2−ε , x 1/2+ε ] we will intro- duce a short sieve weight to maintain the feature that our sums are essentially supported

One could wonder whether assuming the Riemann Hy- pothesis generalized to Dirichlet L-functions (GRH) allows for power-saving error term to be obtained (as is the case for the