On sums and differences of two coprime kth powers
On sums and products of residues modulo p
On sums of five almost equal prime squares
On sums of two kth powers: a mean-square asymptotics over short intervals
On sums of two kth powers: an asymptotic formula for the mean square of the error term
On the -th power mean of with the weight of Gauss sums
The main purpose of this paper is to study the hybrid mean value of and Gauss sums by using the estimates for trigonometric sums as well as the analytic method. An asymptotic formula for the hybrid mean value of and Gauss sums will be proved using analytic methods and estimates for trigonometric sums.
On the Average Number of Direct Factors of a Finite Abelian Group.
On the average number of direct factors of a finite Abelian group
On the average number of direct factors of a finite abelian group (“sur les variété abéliennes”)
On the average number of direct factors of finite abelian groups (II)
On the average number of unitary factors of finite abelian groups
On the Bombieri-Korobov estimate for Weyl sums
On the class number of binary quadratic forms: An omega estimate for the error term.
On the constant factor in Vinogradov's Mean Value Theorem
On the difference between a D. H. Lehmer number and its inverse modulo q
On the discrepancy of some hybrid sequences
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 .