Infinite global fields and the generalized Brauer--Siegel theorem
| dc.creator | Tsfasman, Michael | |
| dc.creator | Vladut, Serge | |
| dc.date | 2002-05-13 | |
| dc.date.accessioned | 2026-07-07T04:48:27Z | |
| dc.date.available | 2026-07-07T04:48:27Z | |
| dc.description | The paper has two purposes. First, we start to develop a theory of infinite global fields, i.e., of infinite algebraic extensions either of ${\mathbb{Q}}$ or of ${\mathbb{F}}_r(t)$. We produce a series of invariants of such fields, and we introduce and study a kind of zeta-function for them. Second, for sequences of number fields with growing discriminant we prove generalizations of the Odlyzko--Serre bounds and of the Brauer--Siegel theorem, taking into account non-archimedean places. This leads to asymptotic bounds on the ratio ${{\log hR}/\log\sqrt{| D|}}$ valid without the standard assumption ${n/\log\sqrt{| D|}}\to 0,$ thus including, in particular, the case of unramified towers. Then we produce examples of class field towers, showing that this assumption is indeed necessary for the Brauer--Siegel theorem to hold. As an easy consequence we ameliorate on existing bounds for regulators. | |
| dc.description | 81 pages, to appear in Moscow Mathematical Journal, v. 2, No. 2 | |
| dc.identifier | https://arxiv.org/abs/math/0205129 | |
| dc.identifier | http://arxiv.org/abs/math/0205129 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64050 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11G20; 11R37; 11R42; 14G05; 14G15 | |
| dc.title | Infinite global fields and the generalized Brauer--Siegel theorem | |
| dc.type | text |