Arithmetic from an advanced perspective: an introduction to the Adeles

Description

Here we offer an introduction to the adele ring over the field of rational numbers Q and highlight some of its beautiful algebraic and topological structure. We then apply this rich structure to revisit some ancient results of number theory and place them within this modern context as well as make some new observations. We conclude by indicating how this theory enables us to extend the basic arithmetic of Q to the more subtle, complicated, and interesting setting of an arbitrary number field.

Links & Downloads

1. http://revistas.pucp.edu.pe/index.php/promathematica/article/view/10278/10723
2. http://repositorio.pucp.edu.pe/index/handle/123456789/95161

Tags

Adele Ring

Nonarchimedean Analysis

P-Adic Numbers

Additional Fields

Identifer	oai:union.ndltd.org:PUCP/oai:tesis.pucp.edu.pe:123456789/95161
Date	25 September 2017
Creators	Burger, Edward B.
Publisher	Pontificia Universidad Católica del Perú
Source Sets	Pontificia Universidad Católica del Perú
Language	Español
Detected Language	English
Type	Artículo
Format	PDF
Source	Pro Mathematica; Vol. 24, Núm. 47-48 (2010); 149-195
Rights	Artículo en acceso abierto, Attribution 4.0 International, https://creativecommons.org/licenses/by/4.0/