Add to ORKGWe show that smooth numbers are equidistributed in arithmetic progressions to moduli of size $x^{66/107-o(1)}$. This overcomes a longstanding barrier of $x^{3/5-o(1)}$ present in previous works of Bombieri-Friedlander-Iwaniec, Fouvry-Tenenbaum, Drappeau, and Maynard. We build on Drappeau's variation of the dispersion method and on exponential sum manipulations of Maynard, ultimately relying on optimized Deshouillers-Iwaniec type estimates for sums of Kloosterman sums.Comment: 49 pages; Improved main result using an adjusted arrangement of exponential sum
In this note, we are interested in obtaining uniform upper bounds for the number of powerful numbers...
The Bombieri-Vinogradov theorem for nilsequences, Discrete Analysis 2021:21, 55 pp. The prime numb...
International audienceWe prove a bound for quintilinear sums of Kloosterman sums, with congruence co...
We prove that the primes below $x$ are, on average, equidistributed in arithmetic progressions to sm...
Let ε>0 be sufficiently small and let 0<η<1/522 . We show that if X is large enough in terms of ε , ...
We denote by ψ(x; q, a) the sum of Λ(n)/n for all n≤x and congruent to a mod q and similarly by ψ(x;...
We denote by ψ(x; q, a) the sum of Λ(n)/n for all n≤x and congruent to a mod q and similarly by ψ(x;...
AbstractIn a recent paper, K. Soundararajan showed, roughly speaking, that the integers smaller than...
AbstractWe establish a result on the large sieve with square moduli. These bounds improve recent res...
In 2020, Roger Baker \cite{Bak} proved a result on the exceptional set of moduli in the prime number...
We show that if an essentially arbitrary sequence supported on an interval containing x integers, is...
We show that there are infinitely many primes p such that p−1 is divisible by a square d2≥pθ for θ=1...
We show that smooth-supported multiplicative functions ƒ are well distributed in arithmetic progress...
In this paper, we prove that, for any positive constants d and e and every large enough x, the inter...
This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Internatio...
In this note, we are interested in obtaining uniform upper bounds for the number of powerful numbers...
The Bombieri-Vinogradov theorem for nilsequences, Discrete Analysis 2021:21, 55 pp. The prime numb...
International audienceWe prove a bound for quintilinear sums of Kloosterman sums, with congruence co...
We prove that the primes below $x$ are, on average, equidistributed in arithmetic progressions to sm...
Let ε>0 be sufficiently small and let 0<η<1/522 . We show that if X is large enough in terms of ε , ...
We denote by ψ(x; q, a) the sum of Λ(n)/n for all n≤x and congruent to a mod q and similarly by ψ(x;...
We denote by ψ(x; q, a) the sum of Λ(n)/n for all n≤x and congruent to a mod q and similarly by ψ(x;...
AbstractIn a recent paper, K. Soundararajan showed, roughly speaking, that the integers smaller than...
AbstractWe establish a result on the large sieve with square moduli. These bounds improve recent res...
In 2020, Roger Baker \cite{Bak} proved a result on the exceptional set of moduli in the prime number...
We show that if an essentially arbitrary sequence supported on an interval containing x integers, is...
We show that there are infinitely many primes p such that p−1 is divisible by a square d2≥pθ for θ=1...
We show that smooth-supported multiplicative functions ƒ are well distributed in arithmetic progress...
In this paper, we prove that, for any positive constants d and e and every large enough x, the inter...
This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Internatio...
In this note, we are interested in obtaining uniform upper bounds for the number of powerful numbers...
The Bombieri-Vinogradov theorem for nilsequences, Discrete Analysis 2021:21, 55 pp. The prime numb...
International audienceWe prove a bound for quintilinear sums of Kloosterman sums, with congruence co...