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arXiv · 2403.11814

On the error in the prime number theorem in short intervals

Ethan Simpson Lee
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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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Ethan Simpson Lee. 2026-07-25. On the error in the prime number theorem in short intervals. https://arxiv.org/abs/2403.11814

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