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
The number of k-ary divisors of a generalized integer
The number of k-ary, (k + 1)-free divisors of an integer.
The number of k-free and k-ary divisors of m which are prime to n.
The number of k-free divisors of an integer
The number of k-free divisors of an integer. II.
The number of prime factors of binomial coefficients
The number of primes in a short interval.
The number of solutions of .
The number of squarefull numbers in an interval
The number of unsieved integers up to x