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arXiv · 2404.06642

Modulus representation of the Riemann $ξ$ function and polynomial inequalities equivalent to the Riemann hypothesis

Wei Sun
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Abstract

We use the Jacobi theta function to give a representation of the modulus of the Riemann $ξ$ function. Based on this modulus representation, we show that the Riemann hypothesis is equivalent to the validity of a family of polynomial inequalities. We also present some preliminary results on the polynomial inequalities.

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Wei Sun. 2024-11-06. Modulus representation of the Riemann $ξ$ function and polynomial inequalities equivalent to the Riemann hypothesis. https://arxiv.org/abs/2404.06642

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