On a conjecture of Pomerance
On a kind of uniform distribution of values of multiplicative functions in residue classes
On a Problem Concerning Two Integer Sequences
On a theorem of Bombieri-Vinogradov type for prime numbers from a thin set
On arithmetic progressions having only few different prime factors in comparison with their length
On distribution of values of σ(n) in residue classes
On Linnik's constant.
On Linnik's constant
On prime divisors of remarkable sequences.
On prime numbers in an arithmetic progression with a prime-power difference
On sets of weak uniform distribution
On the Barban-Davenport-Halberstam theorem. I.
On the Barban-Davenport-Halberstam theorem: IX
On the Barban-Davenport-Halberstam theorem: XI
On the Barban-Davenport-Halberstam theorem: XIII
On the Barban-Davenport-Halberstam theorem: XIV
On the Barban-Davenport-Halberstam theorem: XV
On the Brun-Titchmarsh theorem
The Brun-Titchmarsh theorem shows that the number of primes which are less than x and congruent to a modulo q is less than (C+o(1))x/(ϕ(q)logx) for some value C depending on logx/logq. Different authors have provided different estimates for C in different ranges for logx/logq, all of which give C>2 when logx/logq is bounded. We show that one can take C=2 provided that logx/logq ≥ 8 and q is sufficiently large. Moreover, we also produce a lower bound of size when logx/logq ≥ 8 and is bounded....
On the comparative theory of primes
On the coprimality of certain multiplicative functions