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arXiv · 1803.01964

Harmonic Analysis on the Ad\`ele Ring of $\Q$

Victor A. Aguilar-Arteaga·Manuel Cruz-López·Samuel Estala-Arias
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Abstract

The ring of finite ad\`eles $\Af$ of the rational numbers $\Q$ is obtained in this article as a completion of $\Q$ with respect to a certain non--Archimedean metric. This ultrametric allows to represent any finite ad\`ele as a series generalizing $m$--adic analysis. The description made provides a new perspective for the adelic Fourier analysis on $\Af$, which also permits to introduce new oscillatory integrals. By incorporating the infinite prime, the mentioned results are extended to the complete ring of ad\`eles $\A$} of $\Q$.

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BibTeXRIS

Victor A. Aguilar-Arteaga, Manuel Cruz-López, Samuel Estala-Arias. 2018-03-06. Harmonic Analysis on the Ad\`ele Ring of $\Q$. https://arxiv.org/abs/1803.01964

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