On the average value of divisor sums in arithmetic progressions
No Thumbnail Available
Meeting name
Sponsors
Date
Journal Title
Format
Preprint
Subject
Abstract
We consider very short sums of the divisor function in arithmetic progressions prime to a fixed modulus and show that "on average" these sums are close to the expected value. We also give applications of our result to sums of the divisor function twisted with characters (both additive and multiplicative) taken on the values of various functions, such as rational and exponential functions; in particular, we obtain upper bounds for such twisted sums.