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Resolution of Riemann Hypothesis

Pankaj Mani

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Abstract

The Riemann hypothesis is proved to be true which states that all the non-trivial zeros of Riemann zeta function lie along the line R(z)=1/2 for 0<R(z)<1. The work done here clarifies that there is no need to find out the non-trivial zeros of the Riemann zeta function to prove the Riemann hypothesis true as the Riemann hypothesis must be true for the functional equation satisfied by the zeta function to exist itself structurally in mathematics.

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What this paper is about

The Riemann hypothesis is proved to be true which states that all the non-trivial zeros of Riemann zeta function lie along the line R(z)=1/2 for 0<R(z)<1. The work done here clarifies that there is no need to find out the non-trivial zeros of the Riemann zeta function to prove the Riemann hypothesis true as the Riemann hypothesis must be true for the functional equation satisfied by the zeta function to exist itself structurally in mathematics.

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Available abstract

The Riemann hypothesis is proved to be true which states that all the non-trivial zeros of Riemann zeta function lie along the line R(z)=1/2 for 0<R(z)<1. The work done here clarifies that there is no need to find out the non-trivial zeros of the Riemann zeta function to prove the Riemann hypothesis true as the Riemann hypothesis must be true for the functional equation satisfied by the zeta function to exist itself structurally in mathematics.

Key concepts: Riemann hypothesis, Riemann zeta function, Riemann Xi function, Particular values of Riemann zeta function, Z function, Mathematics, Explicit formulae, Pure mathematics

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