Updating the error term in the prime number theorem

Tim Trudgian

Updating the error term in the prime number theorem

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arxiv 1401.2689 v2 pith:OJH3VWLW submitted 2014-01-13 math.NT

Tim Trudgian This is my paper · ORCID

classification math.NT

keywords giventhetaapplicationsarithmeticcommonconjectureerrorestimate

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abstract

An improved estimate is given for $|\theta(x) -x|$, where $\theta(x) = \sum_{p\leq x} \log p$. Three applications are given: the first to arithmetic progressions that have points in common, the second to primes in short intervals, and the third to a conjecture by C. Pomerance.

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A Dynamical Criterion Equivalent to the Riemann Hypothesis
math.GM 2025-09 reject novelty 3.0 of 10

The paper asserts RH is equivalent to a contraction bound for a prime-counting error functional, but the proof relies on a false large-sieve inequality and a scale-mixing error.

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