# Explicit Estimate on Primes between Consecutive Cubes

@article{Cheng2008ExplicitEO, title={Explicit Estimate on Primes between Consecutive Cubes}, author={Yuanyou Furui Cheng}, journal={arXiv: Number Theory}, year={2008} }

We give an explicit form of Ingham's Theorem on primes in the short intervals, and show that there is at least one prime between every two consecutive cubes $x\sp{3}$ and $(x+1)\sp{3}$ if $\log\log x\ge 15$.

## 8 Citations

An Explicit Result for Primes Between Cubes

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We prove that there is a prime between $n^3$ and $(n+1)^3$ for all $n \geq \exp(\exp(33.217))$. Our new tool which we derive is a version of Landau's explicit formula for the Riemann zeta-function…

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The Riemann zeta function, ζ(s), is central to number theory and our understanding of the distribution of the prime numbers. This thesis presents some of the known results in this area before…

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In this article, we prove an explicit bound for $N(\sigma,T)$, the number of zeros of the Riemann zeta function satisfying $\sigma < \Re s <1 $ and $0 < \Im s < T$. This result provides a significant…

Explicit Estimates in the Theory of Prime Numbers

- Mathematics
- 2016

It is the purpose of this thesis to enunciate and prove a collection of explicit results in the theory of prime numbers.
First, the problem of primes in short intervals is considered. We prove that…

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It is shown that for any fixed i > 0, the Σ i+1-fragment of Presburger arithmetic is complete for ΣiEXP, the i-th level of the weak EXP hierarchy, an analogue to the polynomial-time hierarchy residing between NEXP and EXPSPACE.

A sharpened estimate on the pseudo-Gamma function

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- 2013

The pseudo-Gamma function is a key tool introduced recently by Cheng and Albeverio in the proof of \break the density hypothesis. This function is doubly symmetric, which means that it is…

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