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 .
On integers with a special divisibility property
In this note, we study those positive integers which are divisible by , where is the Carmichael function.
On irregularities in the graph of generalized divisor functions
On isolated, respectively consecutive large values of arithmetic functions
On Mirsky's generalisation of a problem of Evelyn-Linfoot and Page in additive theory of numbers.
On oscillations in the additive divisor problem, 1
On periodic mod p sequences and G-functions (On a conjecture of Ruzsa).
On power-free numbers and polynomials. I.
On power.free numbers and polynomials. II.
On prime divisors of Mersenne numbers