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arXiv · 1510.03416

Deformations of $\Xi(s)=\Xi(1-s)$ and the heat equation

Johannes Löffler
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Abstract

This paper studies deformations of the well-known $\Xi(s)=\Xi(1-s)$ equation for the Riemann $\Xi$ function satisfied by $\Xi_\rho(s):=\int_{0}^\infty\frac{{\d}t}{t}{t^{\frac{s}{2}}}\Psi(t)e^{-\rho\ln^2(t)}$ where ${\Psi(t)=\sum_{n\in\mathbb{N}^+}e^{-\pi{n}^2t}}$.

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Johannes Löffler. 2015-10-13. Deformations of $\Xi(s)=\Xi(1-s)$ and the heat equation. https://arxiv.org/abs/1510.03416

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