On Certain Sums Involving Von Mangoldt's Function In Short Intervals
On cluster primes
On Dirichlet characters of polynomials
On divisors of sums of integers. II.
On gaps between numbers with a large prime factor
On gaps between numbers with a large prime factor. II
On Gelfond’s conjecture about the sum of digits of prime numbers
The goal of this paper is to outline the proof of a conjecture of Gelfond [6] (1968) in a recent work in collaboration with Christian Mauduit [11] concerning the sum of digits of prime numbers, reflecting the lecture given in Edinburgh at the Journées Arithmétiques 2007.
On Grimm's problem relating to factorisation of a block of consecutive integers. II.
On Grimm's problem relating to factorisation of a block of consecutive integers.
On homogeneous multiplicative hybrid problems in number theory
On integers generated by a finite number of fixed primes
On integers with many small prime factors
On linear forms in the logarithms of algebraic numbers
On Popov's explicit formula and the Davenport expansion
We shall establish an explicit formula for the Davenport series in terms of trivial zeros of the Riemann zeta-function, where by the Davenport series we mean an infinite series involving a PNT (Prime Number Theorem) related to arithmetic function with the periodic Bernoulli polynomial weight and PNT arithmetic functions include the von Mangoldt function, Möbius function and Liouville function, etc. The Riesz sum of order or gives the well-known explicit formula for respectively the partial...
On prime factors of sums of integers I
On Representing Integers as Products of the p + 1.
On shifted primes
On sign-changes in the remainder-term of the prime-number formula, II
On sign-changes in the remainder-term of the prime-number formula, I
On sign-changes in the remainder-term of the prime-number formula, IV