Hypergeometric-like Representation of the Zeta-Function of Riemann

Abstract

We present a new expansion of the zeta-function of Riemann. The current formalism -- which combines both the idea of interpolation with constraints and the concept of hypergeometric functions -- can, in a natural way, be generalised within the theory of the zeta-function of Hawking offering thus a variety of applications in quantum field theory, quantum cosmology and statistical mechanics.

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• A new necessary and sufficient condition for the Riemann hypothesis
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• Analysis of Riemann Zeta-Function Zeros using Pochhammer Polynomial Expansions
• A trio of Bernoulli relations, their implications for the Ramanujan polynomials and the zeta constants
• One page proof of the Riemann hypothesis
• Evidence in favor of the Baez-Duarte criterion for the Riemann Hypothesis