Bibliography
- 1
Samuel Broadbent, Habiba Kadiri, Allysa Lumley, Nathan Ng, and Kirsten Wilk. Sharper bounds for the Chebyshev function \(\theta (x)\). Math. Comp., 90(331):2281–2315, 2021.
- 2
Yuanyou Cheng. An explicit upper bound for the Riemann zeta-function near the line \(\sigma =1\). Rocky Mountain J. Math., 29(1):115–140, 1999.
- 3
Juan Arias de Reyna. On the approximation of the zeta function by dirichlet polynomials. 2024.
- 4
Daniele Dona, Harald A. Helfgott, and Sebastian Zuniga Alterman. Explicit \(L^2\) bounds for the Riemann \(\zeta \) function. J. Théor. Nombres Bordx., 34(1):91–133, 2022.
- 5
Pierre Dusart. Explicit estimates of some functions over primes. Ramanujan J., 45(1):227–251, 2018.
- 6
Andrew Fiori, Habiba Kadiri, and Joshua Swidinsky. Sharper bounds for the Chebyshev function \(\psi (x)\). J. Math. Anal. Appl., 527(2):Paper No. 127426, 28, 2023.
- 7
Andrew Fiori, Habiba Kadiri, and Joshua Swidinsky. Sharper bounds for the error term in the prime number theorem. Res. Number Theory, 9(3):Paper No. 63, 19, 2023.
- 8
G. H. Hardy and J. E. Littlewood. The zeros of Riemann’s zeta-function on the critical line. Math. Z., 10:283–317, 1921.
- 9
Habiba Kadiri, Allysa Lumley, and Nathan Ng. Explicit zero density for the Riemann zeta function. J. Math. Anal. Appl., 465(1):22–46, 2018.
- 10
Hugh L. Montgomery and Robert C. Vaughan. Multiplicative number theory. I. Classical theory, volume 97 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 2007.
- 11
J. Barkley Rosser and Lowell Schoenfeld. Approximate formulas for some functions of prime numbers. Illinois J. Math., 6:64–94, 1962.
- 12
Aleksander Simonic. Explicit zero density estimate for the Riemann zeta-function near the critical line. J. Math. Anal. Appl., 491(1):124303, 41, 2020.
- 13
Gérald Tenenbaum. Introduction to analytic and probabilistic number theory. Transl. from the 3rd French edition by Patrick D. F. Ion, volume 163 of Grad. Stud. Math. Providence, RI: American Mathematical Society (AMS), 3rd expanded ed. edition, 2015.
- 14
E. C. Titchmarsh. The theory of the Riemann zeta-function. The Clarendon Press, Oxford University Press, New York, second edition, 1986. Edited and with a preface by D. R. Heath-Brown.