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Primes in explicit short intervals on RH

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Publication:2810682
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DOI10.1142/S1793042116500858zbMath1356.11065arXiv1503.05403MaRDI QIDQ2810682

Adrian W. Dudek, Loïc Grenié, Giuseppe Molteni

Publication date: 3 June 2016

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1503.05403


zbMATH Keywords

primesRiemann hypothesisshort intervals


Mathematics Subject Classification ID

Distribution of primes (11N05)


Related Items

Explicit interval estimates for prime numbers ⋮ PRIMES AND PRIME IDEALS IN SHORT INTERVALS ⋮ Explicit short intervals for primes in arithmetic progressions on GRH ⋮ Unnamed Item ⋮ Primes in arithmetic progressions and semidefinite programming ⋮ Fourier optimization and prime gaps


Uses Software

  • PARI/GP


Cites Work

  • Explicit relations between pair correlation of zeros and primes in short intervals
  • On the first sign change of $\theta (x) -x$
  • Explicit smoothed prime ideals theorems under GRH
  • Sharper Bounds for the Chebyshev Functions θ(x) and ψ(x)
  • On the Riemann hypothesis and the difference between primes
  • Empirical verification of the even Goldbach conjecture and computation of prime gaps up to 4⋅10¹⁸
  • Unnamed Item
  • Unnamed Item
  • Unnamed Item


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