Corrigendum to ‘Explicit interval estimates for prime numbers’

Cully-Hugill, Michaela; Lee, Ethan

doi:10.1090/mcom/3884

Corrigendum to ‘Explicit interval estimates for prime numbers’
HTML articles powered by AMS MathViewer

by Michaela Cully-Hugill and Ethan S. Lee

Math. Comp. 93 (2024), 1019-1025

DOI: https://doi.org/10.1090/mcom/3884

Published electronically: July 19, 2023

HTML | PDF | Request permission

Abstract:

This article corrects a mistake in ‘Explicit interval estimates for prime numbers’, Math. Comp. 91 (2022), 1955–1970. The error was in a closed-form expression for an integral involving the smoothing function. The table of pairs of $(\Delta ,x_0)$ is recomputed for the main theorem, which states that for all $x \geq x_0$ there exists at least one prime in the interval $(x(1-\Delta ^{-1}),x]$.

References

Richard P. Brent, David J. Platt, and Timothy S. Trudgian, Accurate estimation of sums over zeros of the Riemann zeta-function, Math. Comp. 90 (2021), no. 332, 2923–2935. MR 4305374, DOI 10.1090/mcom/3652
Samuel Broadbent, Habiba Kadiri, Allysa Lumley, Nathan Ng, and Kirsten Wilk, Sharper bounds for the Chebyshev function $\theta (x)$, Math. Comp. 90 (2021), no. 331, 2281–2315. MR 4280302, DOI 10.1090/mcom/3643
Michaela Cully-Hugill and Ethan S. Lee, Explicit interval estimates for prime numbers, Math. Comp. 91 (2022), no. 336, 1955–1970. MR 4435953, DOI 10.1090/mcom/3719
Harold Davenport, Multiplicative number theory, 2nd ed., Graduate Texts in Mathematics, vol. 74, Springer-Verlag, New York-Berlin, 1980. Revised by Hugh L. Montgomery. MR 606931, DOI 10.1007/978-1-4757-5927-3
Habiba Kadiri and Allysa Lumley, Short effective intervals containing primes, Integers 14 (2014), Paper No. A61, 18. MR 3274183
Habiba Kadiri, Allysa Lumley, and Nathan Ng, Explicit zero density for the Riemann zeta function, J. Math. Anal. Appl. 465 (2018), no. 1, 22–46. MR 3806689, DOI 10.1016/j.jmaa.2018.04.071
The LMFDB Collaboration, The L-functions and modular forms database, http://www.lmfdb.org, 2020.
H. L. Montgomery and R. C. Vaughan, The large sieve, Mathematika 20 (1973), 119–134. MR 374060, DOI 10.1112/S0025579300004708
Michael J. Mossinghoff and Timothy S. Trudgian, Nonnegative trigonometric polynomials and a zero-free region for the Riemann zeta-function, J. Number Theory 157 (2015), 329–349. MR 3373245, DOI 10.1016/j.jnt.2015.05.010
Dave Platt and Tim Trudgian, The Riemann hypothesis is true up to $3\cdot 10^{12}$, Bull. Lond. Math. Soc. 53 (2021), no. 3, 792–797. MR 4275089, DOI 10.1112/blms.12460
D. J. Platt and T. S. Trudgian, An improved explicit bound on $|\zeta (\frac 12+it)|$, J. Number Theory 147 (2015), 842–851. MR 3276357, DOI 10.1016/j.jnt.2014.08.019
Olivier Ramaré and Yannick Saouter, Short effective intervals containing primes, J. Number Theory 98 (2003), no. 1, 10–33. MR 1950435, DOI 10.1016/S0022-314X(02)00029-X