On non-trivial zeros and Riemann zeta function

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.