On cubic polynomials giving many primes.
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 Dirichlet characters of polynomials
On Dirichlet convolution method.
On distribution of arithmetical functions on the set prime plus one
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 divisors whose sum is a square
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.