On an asymmetric divisor problem with congruence conditions.
On an Effective Order Estimate of the Riemann Zeta Function in the Critical Strip.
On an equation with prime numbers
On an estimate by Weyl and Vinogradov.
On an exponential sum.
On Bourgain's bound for short exponential sums and squarefree numbers
We use Bourgain's recent bound for short exponential sums to prove certain independence results related to the distribution of squarefree numbers in arithmetic progressions.
On certain arithmetic functions involving the greatest common divisor
The paper deals with asymptotics for a class of arithmetic functions which describe the value distribution of the greatest-common-divisor function. Typically, they are generated by a Dirichlet series whose analytic behavior is determined by the factor ζ2(s)ζ(2s − 1). Furthermore, multivariate generalizations are considered.
On certain character sums
On Certain Divisor Functions in Short Intervals
On certain trigonometric sums in several variables.
On character sums and the non-vanishing for s > 0 of Dirichlet L-series belonging to real odd characters χ
On character sums of rational functions over local fields
On characters and polynomials
On characters of order p (mod p²)
On cosine polynomials corresponding to sets of integers
On critical values of twisted Artin -functions
We give a simple proof that critical values of any Artin -function attached to a representation with character are stable under twisting by a totally even character , up to the -th power of the Gauss sum related to and an element in the field generated by the values of and over . This extends a result of Coates and Lichtenbaum as well as the previous work of Ward.
On Cubic Polynomials I.Hua's Estimate of Exponential Sums.
On Cubic Polynomials II. Multiple Exponential Sums.
On Dirichlet series associated with cubic Gauss sums.
On discrete mean values of Dirichlet -functions
Let be a nonprincipal Dirichlet character modulo a prime number and let . Define the mean value We give an identity for which, in particular, shows that for fixed and .