# On the Riemann hypothesis and the difference between primes

@article{Dudek2014OnTR, title={On the Riemann hypothesis and the difference between primes}, author={Adrian W. Dudek}, journal={International Journal of Number Theory}, year={2014}, volume={11}, pages={771-778} }

We prove some results concerning the distribution of primes assuming the Riemann hypothesis. First, we prove the explicit result that there exists a prime in the interval $(x-\frac{4}{\pi} \sqrt{x}...

## 24 Citations

Primes and prime ideals in short intervals

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We prove the analog of Cram\'er's short intervals theorem for primes in arithmetic progressions and prime ideals, under the relevant Riemann Hypothesis. Both results are uniform in the data of the…

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On the assumption of the Riemann hypothesis, we give explicit upper bounds on the difference between consecutive prime numbers.

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We furnish an explicit bound for the prime number theorem in short intervals on the assumption of the Riemann hypothesis.

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Using a smoothing function and recent knowledge on the zeros of the Riemann zeta-function, we compute pairs of $(\Delta, x_0)$ such that for all $x \geq x_0$ there exists at least one prime in the…

The Prime Gaps Between Successive Primes to Ensure that there is Atleast One Prime Between Their Squares Assuming the Truth of the Riemann Hypothesis

- Mathematics
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Based on Dudek’s proof that assumed the truth of the Riemann’s hypothesis, that there exists a prime between {x – (4/pi)( x^ 1/2)(log x)} and x, we determine the size of prime gaps that must exist…

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It is the purpose of this thesis to enunciate and prove a collection of explicit results in the theory of prime numbers.
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We provide an explicit $O(x/T)$ error term for the Riemann--von Mangoldt formula by making results of Wolke (1983) and Ramar\'e (2016) explicit. We also include applications to primes between…

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This paper is the first in a series of four devoted to the abc conjecture, the Riemann Hypothesis, Fermat-Wiles Theorem and its extensions, Fermat Numbers and their generalizations. We propose here a…

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