On the zeros of the Riemann Zeta function

Abstract

This paper is divided into two independent parts. The first part presents new integral and series representations of the Riemaan zeta function. An equivalent formulation of the Riemann hypothesis is given and few results on this formulation are briefly outlined. The second part exposes a totally different approach. Using the new series representation of the zeta function of the first part, exact information on its zeros is provided.

Corrected the sign in formula (6.10) and added few comments. Disappearance of euler constant in all subsequent formulae. Added two references

Cited by in corpus (4)

• On Some Explicit Formulas for Bernoulli Numbers and Polynomials
• On the Hurwitz Zeta Function
• The Riemann Hypothesis: A Qualitative Characterization of the Nontrivial Zeros of the Riemann Zeta Function Using Polylogarithms
• Closed-form formula of Riemann zeta function and eta function for all non-zero given complex numbers via sums of powers of complex functions to disprove Riemann Hypothesis