Explicit Estimates in the Theory of Prime Numbers

@article{Dudek2016ExplicitEI,
  title={Explicit Estimates in the Theory of Prime Numbers},
  author={A. Dudek},
  journal={The Bulletin of the Center for Children's Books},
  year={2016}
}
  • A. Dudek
  • Published 2016
  • Mathematics
  • The Bulletin of the Center for Children's Books
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 there is a prime between consecutive cubes $n^3$ and $(n+1)^3$ for all $n \geq \exp(\exp(33.3))$. To prove this, we first derive an explicit version of the Riemann--von Mangoldt explicit formula. We then assume the Riemann hypothesis and show that there will be a prime in the interval $(x-4/ \pi… Expand
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References

SHOWING 1-10 OF 82 REFERENCES
On the difference between consecutive primes
  • 82
  • Highly Influential
  • PDF
A zero density result for the Riemann zeta function
  • 18
  • PDF
The ternary Goldbach conjecture is true
  • 79
  • PDF
On an inequality of Ramanujan concerning the prime counting function
  • 3
Updating the error term in the prime number theorem
  • 37
  • Highly Influential
  • PDF
Empirical verification of the even Goldbach conjecture and computation of prime gaps up to 4⋅1018
  • 80
  • PDF
An explicit density estimate for Dirichlet L-series
  • 16
  • Highly Influential
  • PDF
The Difference Between Consecutive Primes, II
  • 384
  • PDF
About the cover: On the distribution of primes—Gauss’ tables
  • 5
  • PDF
Explicit Estimate on Primes between Consecutive Cubes
  • 8
  • Highly Influential
  • PDF
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