Sign changes in the prime number theorem

DOI10.1007/s11139-021-00398-8zbMath1485.11130arXiv1910.14203OpenAlexW3135799910MaRDI QIDQ2070385

Dave Platt, Tim Trudgian, Thomas Morrill

Publication date: 24 January 2022

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.14203

zbMATH Keywords

prime number theoremRiemann zeta-functionoscillationsanalytic number theory

Mathematics Subject Classification ID

Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26) Distribution of primes (11N05)

Uses Software

• PARI/GP
• Arb

Cites Work

• An improved explicit bound on \(| \zeta(\frac{1}{2} + i t) |\)
• Changes of sign of the error term in the prime number theorem
• An improved upper bound for the argument of the Riemann zeta-function on the critical line. II
• Mean motions and zeros of almost periodic functions
• Zeroes of partial sums of the zeta-function
• On the first sign change of $\theta (x) -x$
• Isolating some non-trivial zeros of zeta
• The k-functions in multiplicative number theory. I. On complex explicit formulae
• On sign-changes in the remainder-term of the prime-number formula, I
• On sign-changes in the remainder-term of the prime-number formula, II
• The k-functions in multiplicative number theory. V. Changes of sign of some arithmetical error terms
• The Riemann hypothesis is true up to 3·1012
• A still sharper region where $\pi (x)-{\mathrm {li}}(x)$ is positive
• On the difference π(x) - li(x)
• Unnamed Item

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