On Euler-von Mangoldt's equation
On exponential sums involving the divisor function.
On exponential sums with multiplicative coefficients, II
On Exponents in Arithmetical Semigroups.
On extremal sets without coprimes
On -thin sets
On Fabry's gap theorem
By combining Turán’s proof of Fabry’s gap theorem with a gap theorem of P. Szüsz we obtain a gap theorem which is more general then both these theorems.
On factorization of integers with restrictions on the exponents.
On finitely generated monoids of matrices with entries in
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 gaps between numbers with a large prime factor
On gaps between numbers with a large prime factor. II
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 generalized square-full numbers in an arithmetic progression
Let and . Denote by the set of all integers whose canonical prime representation has all exponents
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 Groups of Squarefree Order.
On higher-power moments of E(t)
On higher-power moments of Δ(x)