On the Riemann hypothesis and the difference between primes

DOI10.1142/S1793042115500426zbMath1317.11095arXiv1402.6417WikidataQ56566812 ScholiaQ56566812MaRDI QIDQ5248576

Adrian W. Dudek

Publication date: 8 May 2015

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

Full work available at URL: https://arxiv.org/abs/1402.6417

zbMATH Keywords

Riemann hypothesisprime numbersexplicit formula

Mathematics Subject Classification ID

Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26) Distribution of primes (11N05)

Related Items (14)

Number of prime ideals in short intervals ⋮ Bounds for Zeta and Primes via Fourier Analysis ⋮ Unnamed Item ⋮ A conditional explicit result for the prime number theorem in short intervals ⋮ Explicit interval estimates for prime numbers ⋮ Helson zeta functions for characters with finitely many values ⋮ PRIMES AND PRIME IDEALS IN SHORT INTERVALS ⋮ On the Control of the Navier-Stokes Equations and Related Systems ⋮ Almost-Ramanujan graphs and prime gaps ⋮ Universality and distribution of zeros and poles of some zeta functions ⋮ Primes in explicit short intervals on RH ⋮ On zeroes and poles of Helson zeta functions ⋮ Primes in arithmetic progressions and semidefinite programming ⋮ Fourier optimization and prime gaps

Cites Work

• A note on the differences between consecutive primes
• Short effective intervals containing primes
• On the Difference π(x ) − lix (II)
• An improved upper bound for the argument of the Riemann zeta-function on the critical line
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