The verification of a Riemann Hypothesis in the negative half of the complex plane

William Fidler

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Akademische Arbeit aus dem Fachbereich Mathematik - Analysis, Note: 2.00, , Sprache: Deutsch, Abstract: In this paper, a new zeta...

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Akademische Arbeit aus dem Fachbereich Mathematik - Analysis, Note: 2.00, , Sprache: Deutsch, Abstract: In this paper, a new zeta function is derived. The function is a novel form of a Riemann zeta function. Whilst all the exponents of the terms in the denominators in the series are complex numbers, the function can be shown to be real, zero or complex at any locations of interest in the complex plane. In particular, if regions having the dimensions of Riemann's Critical Strip are formed, where the line of symmetry passes through a trivial zero of Riemann's zeta function, it is shown that zeros values of this new function will only be found along these lines of symmetry, and, indeed, nowhere else in the negative half of the complex plane. It is then considered that this constitutes verification of a Riemann Hypothesis for this function in these regions.