On lattice points in large convex bodies
On Lehmer's problem and Dedekind sums
Let be an odd prime and a fixed integer with . For each integer with , it is clear that there exists one and only one with such that (mod ). Let denote the number of all solutions of the congruence equation (mod ) for , in which and are of opposite parity, where is defined by the congruence equation . The main purpose of this paper is to use the properties of Dedekind sums and the mean value theorem for Dirichlet -functions to study the hybrid mean value problem involving...
On linear recursion and pseudorandomness
On Linnik's approximation to Goldbach's problem, I
On Linnik's theorem on Goldbach numbers in short intervals and related problems
Linnik proved, assuming the Riemann Hypothesis, that for any , the interval contains a number which is the sum of two primes, provided that is sufficiently large. This has subsequently been improved to the same assertion being valid for the smaller gap , the added new ingredient being Selberg’s estimate for the mean-square of primes in short intervals. Here we give another proof of this sharper result which avoids the use of Selberg’s estimate and is therefore more in the spirit of Linnik’s...
On mean values of L-functions and short character sums with real characters
On Mellin-Ramanujan expansions
On nonary cubic forms.
On nonary cubic forms: III.
On pairs of additive cubic equations.
On polynomial Gauss sums (mod Pⁿ), n ≥ 2
On polynomials in primes and J. Bourgain's circle method approach to ergodic theorems II
On rationality of Jacobi sums
On real characters
On recurrence properties of certain lacunary series. I. General results.
On recurrence properties of certain lacunary series. II. General results.
On Selberg's Eigenvalue Conjecture.
On Shioda's problem about Jacobi sums
On Shioda's problem about Jacobi sums II
On solutions of polynomial congruences