Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Proof to the Riemann Hypothesis Using a Simplified Xi-Function   The Riemann hypothesis has been of great interest in the mathematics
community since it was proposed by Bernhard Riemann in 1859, and makes
important implications about the distribution of prime numbers. We have proved
the Riemann hypothesis in this paper. First, we briefly reviewed the simplified
Riemann $\xi(s)$ function. Then we showed the $\xi(s)$ function has a
polynomial decreasing rate, simple zeros and simple stationary points in the
critical line. After that, we applied the idea of bisection search to break up
the complex domain into several sub-domains, in which the imaginary part of
$\xi(s)$ takes different signs. Using the Cauchy-Riemann equations we found
that the zeros of the $\xi(s)$ function cannot locate outside the critical
line, and thus proved that the Riemann hypothesis is true. At the end, we gave
some comments to the P\'olya's counterexample.

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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph