The distribution of primes satisfying the condition
The distribution of sequences in arithmetic progressions
The distribution of squarefree numbers.
The distribution of square-free numbers
The Erdős and Halberstam theorems for Drinfeld modules of any rank (with an appendix by Hugh Thomas)
The generalization and proof of Bertrand's postulate.
The Goldston-Pintz-Yıldırım sieve and maximal gaps
The greatest prime factor of
The greatest prime factor of the integers in an interval
The k-functions in multiplicative number theory. I. On complex explicit formulae
The k-functions in multiplicative number theory. II. Uniform distribution of zeta zeros
The k-functions in multiplicative number theory. III. Uniform distribution of zeta zeros; discrepancy
The k-functions in multiplicative number theory. IV. On a method of A. E. Ingham
The k-functions in multiplicative number theory. V. Changes of sign of some arithmetical error terms
The k-tuple jumping champions among consecutive primes
The least prime in an arithmetic progression with prime difference.
The least square-free number in an arithmetic progression.
The localisation of primes in arithmetic progressions of irrational modulus
A new method for counting primes in a Beatty sequence is proposed, and it is shown that an asymptotic formula can be obtained for the number of such primes in a short interval.
The mean behavior of primes in arithmetic progressions.
The -th prime asymptotically
A new derivation of the classic asymptotic expansion of the -th prime is presented. A fast algorithm for the computation of its terms is also given, which will be an improvement of that by Salvy (1994).Realistic bounds for the error with , after having retained the first terms, for , are given. Finally, assuming the Riemann Hypothesis, we give estimations of the best possible such that, for , we have where is the sum of the first four terms of the asymptotic expansion.