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)
On higher-power moments of Δ(x) (II)
On higher-power moments of Δ(x) (III)
On homogeneous multiplicative hybrid problems in number theory
On ideals free of large prime factors
In 1989, E. Saias established an asymptotic formula for with a very good error term, valid for , , We extend this result to an algebraic number field by obtaining an asymptotic formula for the analogous function with the same error term and valid in the same region. Our main objective is to compare the formulae for and and in particular to compare the second term in the two expansions.
On indefinite quadratic forms in four variables
On integers generated by a finite number of fixed primes