On an asymptotic formula of Srinivasa Ramanujan
On an estimate of Walfisz and Saltykov for an error term related to the Euler function
The technique developed by A. Walfisz in order to prove (in 1962) the estimate for the error term related to the Euler function is extended. Moreover, the argument is simplified by exploiting works of A.I. Saltykov and of A.A. Karatsuba. It is noted in passing that the proof proposed by Saltykov in 1960 of is erroneous and once corrected “only” yields Walfisz’ result. The generalizations obtained can be applied to error terms related to various classical - and less classical - arithmetical...
On asymptotically correlated -multiplicative functions.
On Bombieri's asymptotic sieve
On Bourgain's bound for short exponential sums and squarefree numbers
We use Bourgain's recent bound for short exponential sums to prove certain independence results related to the distribution of squarefree numbers in arithmetic progressions.
On certain arithmetic functions involving the greatest common divisor
The paper deals with asymptotics for a class of arithmetic functions which describe the value distribution of the greatest-common-divisor function. Typically, they are generated by a Dirichlet series whose analytic behavior is determined by the factor ζ2(s)ζ(2s − 1). Furthermore, multivariate generalizations are considered.
On Certain Divisor Functions in Short Intervals
On certain functions that generalize von Mangoldt’s function
On certain sum in number theory
On consecutive Farey arcs
On consecutive Farey arcs II
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