Shubhrajit Bhattacharya

Correlations of error terms for weighted prime counting functions

Standard prime-number counting functions, such as ψ(x), θ(x), and π(x), have error terms with limiting logarithmic distributions once suitably normalized. The same is true of weighted versions of those sums, like πr(x)=∑p≤x1p and πℓ(x)=∑p≤xlog(1−1p)−1, that were studied by Merten...