• Corpus ID: 218581575

# A New Proof of Newman's Conjecture and a Generalization

@article{Dobner2020ANP,
title={A New Proof of Newman's Conjecture and a Generalization},
author={Alexander Dobner},
journal={arXiv: Number Theory},
year={2020}
}
Newman's conjecture (proved by Rodgers and Tao in 2018) concerns a certain family of deformations $\{\xi_t(s)\}_{t \in \mathbb{R}}$ of the Riemann xi function for which there exists an associated constant $\Lambda \in \mathbb{R}$ (called the de Bruijn-Newman constant) such that all the zeros of $\xi_t$ lie on the critical line if and only if $t \geq \Lambda$. The Riemann hypothesis is equivalent to the statement that $\Lambda \leq 0$, and Newman's conjecture states that $\Lambda \geq 0$. In…

## Figures from this paper

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THE DE BRUIJN–NEWMAN CONSTANT IS NON-NEGATIVE
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For each $t\in \mathbb{R}$, we define the entire function $$\begin{eqnarray}H_{t}(z):=\int _{0}^{\infty }e^{tu^{2}}\unicode[STIX]{x1D6F7}(u)\cos (zu)\,du,\end{eqnarray}$$ where

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