In this paper, we prove that, for any positive constants d and e and every large enough x, the interval [x, x + root x(log x)(7/3+delta)] contains numbers whose all prime factors are smaller than x(epsilon)
AbstractSelberg has shown on the basis of the Riemann hypothesis that for every ε > 0 most intervals...
In this paper, we establish a quite general mean value result of arithmetic functions over short int...
We show that smooth numbers are equidistributed in arithmetic progressions to moduli of size $x^{66/...
In this note, we are interested in obtaining uniform upper bounds for the number of powerful numbers...
We introduce a general result relating "short averages" of a multiplicative function to "long averag...
We show that, for the M\"obius function $\mu(n)$, we have $$ \sum_{x < n\leq x+x^{\theta}}\mu(n)=o(x...
AbstractWe consider the problem of estimating the number Ψ(x, xx) − Ψ(x − xβ, xx) of integers in the...
We introduce a general result relating “short averages” of a multiplicative function to “long averag...
We introduce a general result relating “short averages” of a multiplicative function to “long averag...
This paper is concerned with the number of primes in short intervals. We prove that for every $\thet...
We introduce a general result relating “short averages” of a multiplicative function to “long averag...
AbstractIn a recent paper, K. Soundararajan showed, roughly speaking, that the integers smaller than...
Let E-k be the set of positive integers having exactly k prime factors. We show that almost all inte...
The variance of primes in short intervals relates to the Riemann Hypothesis, Montgomery's Pair Corre...
Assuming the Riemann Hypothesis we prove that the interval $[N,N+H]$ contains an integer which ...
AbstractSelberg has shown on the basis of the Riemann hypothesis that for every ε > 0 most intervals...
In this paper, we establish a quite general mean value result of arithmetic functions over short int...
We show that smooth numbers are equidistributed in arithmetic progressions to moduli of size $x^{66/...
In this note, we are interested in obtaining uniform upper bounds for the number of powerful numbers...
We introduce a general result relating "short averages" of a multiplicative function to "long averag...
We show that, for the M\"obius function $\mu(n)$, we have $$ \sum_{x < n\leq x+x^{\theta}}\mu(n)=o(x...
AbstractWe consider the problem of estimating the number Ψ(x, xx) − Ψ(x − xβ, xx) of integers in the...
We introduce a general result relating “short averages” of a multiplicative function to “long averag...
We introduce a general result relating “short averages” of a multiplicative function to “long averag...
This paper is concerned with the number of primes in short intervals. We prove that for every $\thet...
We introduce a general result relating “short averages” of a multiplicative function to “long averag...
AbstractIn a recent paper, K. Soundararajan showed, roughly speaking, that the integers smaller than...
Let E-k be the set of positive integers having exactly k prime factors. We show that almost all inte...
The variance of primes in short intervals relates to the Riemann Hypothesis, Montgomery's Pair Corre...
Assuming the Riemann Hypothesis we prove that the interval $[N,N+H]$ contains an integer which ...
AbstractSelberg has shown on the basis of the Riemann hypothesis that for every ε > 0 most intervals...
In this paper, we establish a quite general mean value result of arithmetic functions over short int...
We show that smooth numbers are equidistributed in arithmetic progressions to moduli of size $x^{66/...
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