On the error in the prime number theorem in short intervals

Abstract

Assuming the Riemann Hypothesis, we derive explicit bounds for the error terms in short interval analogues of the prime number theorem using a new smoothing argument. Our results improve upon earlier bounds in both constant terms and applicable ranges. In addition, we apply our bounds to establish sharper conditional bounds for a broad class of weighted sums over primes in a short interval.

arXiv commentFacelifted and results extended based on feedback. As usual: 15 pages, comments and suggestions are warmly welcomed!