AbstractWe prove a Bombieri–Vinogradov type result for linear exponential sums over primes. Then we apply it to show that, for any irrational α and some θ>0, there are infinitely many primes p such that p+2 has at most two prime factors and ‖αp+β‖<p−θ
AbstractIt is conjectured that all sufficiently large integers satisfying some necessary congruence ...
For a set of primes P, let Ψ(x;P) be the number of positive integers n≤x all of whose prime factors ...
After the proof of Zhang about the existence of infinitely many bounded gaps between consecutive pri...
AbstractLet f(x) be a real valued polynomial in x of degree k⩾4 with leading coefficient α. In this ...
AbstractA sum-product equation is considered in prime fields. We bound a multilinear exponential sum...
AbstractLet Pr denote an almost-prime with at most r prime factors, counted according to multiplicit...
AbstractWe consider the ternary Goldbach problem with two prime variables of the form k2+m2+1 and fi...
AbstractIn this paper, we are able to sharpen Hua's classical result by showing that each sufficient...
We prove that the only solutions to the equation σ(n)=2φ(n) with at most three distinct prime factor...
We prove that the only solutions to the equation σ(n)=2φ(n) with at most three distinct prime factor...
summary:In this note, we show that the counting function of the number of composite positive integer...
summary:In this note, we show that the counting function of the number of composite positive integer...
AbstractIn this paper we continue our study, begun in G. Harman and A.V. Kumchev (2006) [10], of the...
We refine a result of the last two Authors on a Diophantine approximation problem with two primes a...
AbstractWe use the explicit formula of V. Shevelev for the best possible exponent α(m) in the error ...
AbstractIt is conjectured that all sufficiently large integers satisfying some necessary congruence ...
For a set of primes P, let Ψ(x;P) be the number of positive integers n≤x all of whose prime factors ...
After the proof of Zhang about the existence of infinitely many bounded gaps between consecutive pri...
AbstractLet f(x) be a real valued polynomial in x of degree k⩾4 with leading coefficient α. In this ...
AbstractA sum-product equation is considered in prime fields. We bound a multilinear exponential sum...
AbstractLet Pr denote an almost-prime with at most r prime factors, counted according to multiplicit...
AbstractWe consider the ternary Goldbach problem with two prime variables of the form k2+m2+1 and fi...
AbstractIn this paper, we are able to sharpen Hua's classical result by showing that each sufficient...
We prove that the only solutions to the equation σ(n)=2φ(n) with at most three distinct prime factor...
We prove that the only solutions to the equation σ(n)=2φ(n) with at most three distinct prime factor...
summary:In this note, we show that the counting function of the number of composite positive integer...
summary:In this note, we show that the counting function of the number of composite positive integer...
AbstractIn this paper we continue our study, begun in G. Harman and A.V. Kumchev (2006) [10], of the...
We refine a result of the last two Authors on a Diophantine approximation problem with two primes a...
AbstractWe use the explicit formula of V. Shevelev for the best possible exponent α(m) in the error ...
AbstractIt is conjectured that all sufficiently large integers satisfying some necessary congruence ...
For a set of primes P, let Ψ(x;P) be the number of positive integers n≤x all of whose prime factors ...
After the proof of Zhang about the existence of infinitely many bounded gaps between consecutive pri...
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