Sign changes in the prime number theorem

ACRC. BlueCrystal Phase 3 User Guide. (2015)

Batut, C., Belabas, K., Bernardi, D., Cohen, H., Olivier, M.: User’s Guide to PARI-GP (2000)

Brent, R.P., Platt, D.J., Trudgian, T.S.: The mean square of the error term in the prime number theorem. Submitted. Preprint available at arXiv:2008.06140

Demichel, P., Saouter, Y., Trudgian, T.: A still sharper region where $$\pi (x) - \rm li(x)$$ is positive. Math. Comp. 84(295), 2433–2446 (2015)

Jessen, B., Tornehave, H.: Mean motions and zeros of almost periodic functions. Acta Math. 77, 137–279 (1945)

Johansson, F.: Arb: a C library for ball arithmetic. ACM Commun. Comput. Algebra 4(47), 166–169 (2013)

Kaczorowski, J.: On sign-changes in the remainder-term of the prime-number formula I. Acta Arithm. 44(4), 365–377 (1984)

Kaczorowski, J.: On sign-changes in the remainder-term of the prime-number formula II. Acta Arithm. 45(1), 65–74 (1985)

Kaczorowski, J.: The $$k$$-functions in multiplicative number theory I. Acta Arithm. 56(3), 195–211 (1990)

Kaczorowski, J.: The $$k$$-functions in multiplicative number theory, V. Acta Arithm. 59(1), 38–58 (1991)

Kaczorowski, J.: Boundary values of Dirichlet series and the distribution of primes. European Congress of Mathematics, Vol. 1 (Budapest, 1996). Progress in Mathematics, 168, vol. 1, pp. 237–254. Birkhäuser, Basel (1996)

Lehman, R.S.: On the difference $$\pi (x) - \rm li(x)$$. Acta Arithm. 11, 397–410 (1966)

Littlewood, J.E.: Sur la distribution des nombres premiers. Comptes Rendus 158, 1869–1872 (1914)

Montgomery, H.L., Vorhauer, U.M.A.: Changes of sign of the error term in the prime number theorem. Funct. Approx. Comment. Math. 35, 235–247 (2006)

Platt, D.J.: Isolating some non-trivial zeros of $$\zeta $$. Math. Comp. 307(86), 2449–2467 (2017)

Platt, D.J., Trudgian, T.S.: The Riemann hypothesis is true up to $$3 \cdot 10^{12}$$. Bull. Lond. Math. Soc. https://doi.org/10.1112/blms.12460

Platt, D.J., Trudgian, T.S.: An improved explicit bound on $$|\zeta (\frac{1}{2} + it)|$$. J. Number Theory 147, 842–851 (2015)

Platt, D.J., Trudgian, T.S.: On the first sign change of $$\theta (x) -x$$. Math. Comp. 85(299), 1539–1547 (2016)

Platt, D.J., Trudgian, T.S.: Zeroes of partial sums of the zeta-function. LMS J. Comput. Math. 19(1), 37–41 (2016)

Pólya, G.: Über das Vorzeichen des Restgliedes im Primzahlsatz. Number Theory and Analysis (Papers in Honor of Edmund Landau), pp. 233–244. Plenum, New York (1969)

Trudgian, T.S.: An improved upper bound for the argument of the Riemann zeta-function on the critical line II. J. Number Theory 134, 280–292 (2014)