On the Riemann Hypotheses

Details On the Riemann Hypotheses On the Riemann Hypotheses

2009-06-25

arxiv.org/abs/0906.4604v11

Mathematics

General Mathematics

7 pages

Scientific paper

In this work we present a proof to the Riemann hypothesis. In our proof, the Fourier integral representation for the Riemann Xi function $\Xi(s)$ and the fact that a certain elementary function defined by the Euler Gamma function $\Gamma(z)$ has no zeros in the critical strip are essential. It seems that our approach could also apply to the Generalized Riemann hypothesis for the Dirichlet $L$-series with primitive characters.

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