On Artin's conjecture.
On Artin's Conjecture and Euclid's Algorithm in Global Fields.
On asymptotically correlated -multiplicative functions.
On Binary Equations.
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 Certain Sums Involving Von Mangoldt's Function In Short Intervals
On characters and polynomials
On characters of order p (mod p²)
On Chebyshev's inequalities for Beurling's generalized primes
On cluster primes
On composite n for which φ(n) | n -1
On consecutive Farey arcs
On consecutive Farey arcs II
On consecutive integers divisible by the number of their divisors
We prove that there are no strings of three consecutive integers each divisible by the number of its divisors, and we give an estimate for the number of positive integers n ≤ x such that each of n and n + 1 is a multiple of the number of its divisors.
On Consecutive k'th Power Residues.