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arXiv · 2310.15210

Monotonicity of the imaginary part of the Riemann $\xi$ function in the region $S$

Jun Liu
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Abstract

This paper proves that the imaginary part of the Riemann $\xi$ function is strictly monotonic with $b$ in the region $S = \{t|t=a+bi,\ 0\leq a \leq 9.508,\ -1/2<b<1/2\}$. That leads to Im($\xi$)=0 being true only when $b=0$ in $S$.

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Jun Liu. 2023-10-23. Monotonicity of the imaginary part of the Riemann $\xi$ function in the region $S$. https://arxiv.org/abs/2310.15210

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