On non-trivial zeros and Riemann zeta function ∗

Bertrand  Wong

doi:10.48165/bpas.2023.42E.1.7

Authors

Bertrand Wong Department of Science and Technology, Eurotech, Singapore Branch, Singapore.

DOI:

https://doi.org/10.48165/bpas.2023.42E.1.7

Keywords:

Complex numbers, complex plane, primes, Riemann zeta function, non trivial zeros, error, estimate of quantity of primes

Abstract

This paper examines the mysterious non-trivial zeros of the Riemann zeta function ζ and explains their role, e.g., in the computation of the error term in Riemann’s J function for estimating the quantity of primes less than a given number. The paper also explains the close connection between the Riemann zeta function ζ and the prime numbers.

References

Edwards, H. M. (2001). Riemann’s Zeta Function, Dover Publications Inc., New York. [2] Hardy, G. H. and Wright, E. M. (1979). An Introduction to Theory of Numbers, Clarendon Press, Oxford, England.

Ivic, A. (2003). The Riemann Zeta-Function: Theory and Applications, Dover Publications Inc., New York.

Riemann, B. (1859). On the number of prime numbers less than a given quantity, Berlin Academy of Sciences, Berlin.

Wong, B. (2022). Non-trivial zeros of Riemann zeta function and Riemann hypothesis, Bull. Pure Appl. Sci. Sect. E Math. Stat., 41E(1), 88-ff99.