Divisors in windows and the Euler--Mascheroni constant

David Victor Feldman

For $0<c<1$ the number of divisors of $q$ below $q^c$ averages, over $q\le B$, to $c\log B+(\gamma -c)+O(B^{-\min (c,1-c)})$, where $\gamma$ denotes the Euler--Mascheroni constant. Consequen…