On some divisor problems
On sum-product representations in
The purpose of this paper is to investigate efficient representations of the residue classes modulo , by performing sum and product set operations starting from a given subset of . We consider the case of very small sets and composite for which not much seemed known (nontrivial results were recently obtained when is prime or when log ). Roughly speaking we show that all residue classes are obtained from a -fold sum of an -fold product set of , where and , provided the residue sets...
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.