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arXiv · 2406.06066

Note on the asymptotic of the auxiliary function

Juan Arias de Reyna
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Abstract

To define an explicit regions without zeros of $\mathop{\mathcal R}(s)$, in a previous paper we obtained an approximation to $\mathop{\mathcal R}(s)$ of type $f(s)(1+U)$ with $|U|< 1$. But this $U$ do not tend to zero when $t\to+\infty$. In the present paper we get an approximation of the form $f(s)(1+o(t))$. We precise here Siegel's result, following his reasoning. This is essential to get the last Theorems in Siegel's paper about $\mathop{\mathcal R}(s)$.

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Juan Arias de Reyna. 2024-06-10. Note on the asymptotic of the auxiliary function. https://arxiv.org/abs/2406.06066

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