2018/02/28 by Mastrostefano, Daniele
#11N05 #11N36 #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1802.10327
We prove that for every nonnegative integer m there exists an ε>0 such that if λ∈ (0,ε] and x is sufficiently large in terms of m, then the number of positive integers n≤ x for which the interval [n,n+λlog n] contains exactly m primes is at least a constant times x/log x. This improves a result of T. Freiberg, when λ is small.