On non-trivial zeros and Riemann zeta
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On non-trivial zeros and Riemann zeta
Bertrand Wong1
BPAS-E-Math and Stat. Vol.42E(1) June 2023
DOI: 10.48165/bpas.2023.42E.1.7
Page: . 57-60
Description
Description
On non-trivial zeros and Riemann zeta
Bertrand Wong1
- Department of Science and Technology, Eurotech, Singapore Branch, Singapore.
- E-mail: bwong8@singnet.com.sg
Communicated, edited and typeset in Latex by Lalit Mohan Upadhyaya (Editor-in-Chief).
Received November 25, 2022 / Revised May 21, 2023 / Accepted June 04, 2023. Online First Published
on June 30, 2023 at https://www.bpasjournals.com/.
Corresponding author Bertrand Wong, E-mail: bwong8@singnet.com.sg
Abstract
This paper examines the mysterious non-trivial zeros of the Riemann zeta function $\zeta$  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 $\zeta$   and the prime numbers.
 Key words Complex numbers, complex plane, primes, Riemann zeta function, nontrivial zeros, error, estimate of quantity of primes.
 2020 Mathematics Subject Classification 11A41, 11A99.
