Prime Number Theorem And ...

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.