On the intervals between numbers that are sums of two squares. III.
On the intervals between numbers that are sums of two squares: IV.
On the irrationality of a divisor function series.
On the iterates of the sum of exponential divisors.
On the iteration of . (Sur l'itéré de .)
On the k-free divisor problem
On the k-free divisor problem (II)
On the largest -primitive subset of .
On the largest prime factor of integers
On the largest prime factor of
For an integer we denote by the largest prime factor of . We obtain several upper bounds on the number of solutions of congruences of the form and use these bounds to show that
On the largest prime factor of the partition function of n
On the largest prime factors of n and n+1.
On the largest prime factors of n and n+1. (Short Communication).
On the Laurent Coefficients of Certain Dirichlet Series
On the least almost-prime in arithmetic progression
Let denote an almost-prime with at most prime factors, counted according to multiplicity. Suppose that and are positive integers satisfying . Denote by the least almost-prime which satisfies . It is proved that for sufficiently large , there holds This result constitutes an improvement upon that of Iwaniec (1982), who obtained the same conclusion, but for the range in place of .
On the least almost-prime in arithmetic progressions
Let denote a positive integer with at most prime factors, counted according to multiplicity. For integers , such that , let denote the least in the arithmetic progression . It is proved that for sufficiently large , we have This result constitutes an improvement upon that of J. Li, M. Zhang and Y. Cai (2023), who obtained
On the least prime in an arithmetic progression and estimates for the zeros of Dirichlet L-functions
On the least prime in an arithmetic progression. I: The basic theorem
On the least prime in an arithmetic progression. II: The Deuring- Heilbronn theorem
On the least quadratic non-residue of a prime p ... 3 (mod 4).