On Consecutive k'th Power Residues.
On differences of two squares
The arithmetic function ρ(n) counts the number of ways to write a positive integer n as a difference of two squares. Its average size is described by the Dirichlet summatory function Σn≤x ρ(n), and in particular by the error term R(x) in the corresponding asymptotics. This article provides a sharp lower bound as well as two mean-square results for R(x), which illustrates the close connection between ρ(n) and the number-of-divisors function d(n).
On distribution of values of σ(n) in residue classes
On Divisor Problems in Connection with Squarefree Numbers.
On divisors of sums of integers. II.
On exponential sums involving the divisor function.
On exponential sums with multiplicative coefficients, II
On Exponents in Arithmetical Semigroups.
On -thin sets
On factorization of integers with restrictions on the exponents.
On fluctuations in the mean of a sum-of-divisors function
On fluctuations in the mean of a sum-of-divisors function, II
I give explicit values for the constant implied by an Omega-estimate due to Chen and Chen [CC] on the average of the sum of the divisors of n which are relatively coprime to any given integer a.
On Gelfond’s conjecture about the sum of digits of prime numbers
The goal of this paper is to outline the proof of a conjecture of Gelfond [6] (1968) in a recent work in collaboration with Christian Mauduit [11] concerning the sum of digits of prime numbers, reflecting the lecture given in Edinburgh at the Journées Arithmétiques 2007.
On Grimm's problem relating to factorisation of a block of consecutive integers. II.
On Grimm's problem relating to factorisation of a block of consecutive integers.
On higher-power moments of E(t)
On higher-power moments of Δ(x)
On higher-power moments of Δ(x) (II)
On higher-power moments of Δ(x) (III)
On integers n with for .