On the distribution of distances between the points of affine curves over finite fields.
On the distribution of exponential sums.
On the distribution of -integers in Piatetski-Shapiro sequences
A natural number is said to be a -integer if , where and is not divisible by the th power of any prime. We study the distribution of such -integers in the Piatetski-Shapiro sequence with . As a corollary, we also obtain similar results for semi--free integers.
On the distribution of modulo one
In this paper, we give a new upper-bound for the discrepancyfor the sequence , when and .
On the distribution of primitive Pythagorean triangles
On the Distribution of Square-Full and Cube-Full Integers.
On the distribution of squares of integral quaternions II
On the divisor function over Piatetski-Shapiro sequences
Let be an integer part of and be the number of positive divisor of . Inspired by some results of M. Jutila (1987), we prove that for , where is the Euler constant and is the Piatetski-Shapiro sequence. This gives an improvement upon the classical result of this problem.
On the estimates of double exponential sums
On the estimation of certain exponential sums
On the mean squared modulus of a Dirichlet L-function over a short segment of the critical line
On the parity of k-th powers modulo p. A generalization of a problem of Lehmer
On the set .
On the set of distances between two sets over finite fields.
On the smallest pseudopower
On twisted exponential sums.
On two problems of Mordell about exponential sums
Oscillations of Hecke eigenvalues at shifted primes.
In this paper, we are interested in exploring the cancellation of Hecke eigenvalues twisted with an exponential sums whose amplitude is √n at prime arguments.
Piatetski-Shapiro meets Chebotarev
Let K be a finite Galois extension of the field ℚ of rational numbers. We prove an asymptotic formula for the number of Piatetski-Shapiro primes not exceeding a given quantity for which the associated Frobenius class of automorphisms coincides with any given conjugacy class in the Galois group of K/ℚ. In particular, this shows that there are infinitely many Piatetski-Shapiro primes of the form a² + nb² for any given natural number n.
Piatetski-Shapiro sequences