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 large sieve in Riemann surfaces
The largest prime factor of X³ + 2
Improving on a theorem of Heath-Brown, we show that if X is sufficiently large then a positive proportion of the values n³ + 2: n ∈ (X,2X] have a prime factor larger than .
The least pair of consecutive character non-residues.
The least prime in an arithmetic progression with prime difference.
The least prime primitive root and the shifted sieve
The least square-free number in an arithmetic progression.
The level of distribution of the special values of L-functions
The linear sieve, revisited
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 mean square of the error term in a generalization of Dirichlet's divisor problem
The multiplicative group of rationals generated by the shifted primes, I.
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.
The number of commutative semigroups of order N.
The number of cube-full numbers in an interval