Asymptotic behaviour of the Euler-Kronecker constant
| dc.creator | Tsfasman, Michael | |
| dc.date | 2005-03-17 | |
| dc.date | 2005-10-22 | |
| dc.date.accessioned | 2026-07-07T06:39:36Z | |
| dc.date.available | 2026-07-07T06:39:36Z | |
| dc.description | This appendix to the beautiful paper of Ihara puts it in the context of infinite global fields of our papers. We study the behaviour of Euler--Kronecker constant $γ\_{K}$ when the discriminant (respectively, the genus) tends to infinity. Results of our paper easily give us good lower bounds on the ratio ${γ\_{K}/\log\sqrt{| d\_{K}|}}$. In particular, for number fields, under the generalized Riemann hypothesis we prove $$\liminf{γ\_{K}\over\log\sqrt{| d\_{K}|}}\ge -0.26049...$$ Then we produce examples of class field towers, showing that $$\liminf{γ\_{K}\over\log\sqrt{| d\_{K}|}}\le -0.17849...$$} | |
| dc.identifier | https://arxiv.org/abs/math/0503347 | |
| dc.identifier | http://arxiv.org/abs/math/0503347 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/101137 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | MSC 11G20, 11R37, 11R42, 14G05, 14G15, 14H05 | |
| dc.title | Asymptotic behaviour of the Euler-Kronecker constant | |
| dc.type | text |