Greg Martin

Joint Distributions of Error Terms for Primes in Arithmetic Progressions Modulo 11

We provide a formula for the logarithmic density of the set of positive real numbers on which two prime counting functions $ψ(x;q,a)$ and $ψ(x;q,b)$ are simultaneously larger than their asymptotic main terms, as well as a method for calculating the numerical values of such densit...

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...