On the error in the prime number theorem in short intervals

2024/03/18 by Ethan Simpson Lee, Lee, Ethan Simpson
Computer Science · #Distributed and Parallel Computing Systems #Computational Physics and Python Applications

paper · pdf · doi:10.48550/arxiv.2403.11814

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.

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