On the Northcott property for special values of L-functions
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2020
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913683981991936 |
|---|---|
| author | Pazuki, Fabien Pengo, Riccardo |
| author_facet | Pazuki, Fabien Pengo, Riccardo |
| contents | We propose an investigation on the Northcott, Bogomolov and Lehmer properties for special values of L-functions. We first introduce an axiomatic approach to these three properties. We then focus on the Northcott property for special values of L-functions. In the case of L-functions of pure motives, we prove a Northcott property for special values located at the left of the critical strip, assuming that the L-functions in question satisfy some expected properties. Inside the critical strip, focusing on the Dedekind zeta function of number fields, we prove that such a property does not hold for the special value at one, but holds for the special value at zero, and we give a related quantitative estimate in this case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_00542 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On the Northcott property for special values of L-functions Pazuki, Fabien Pengo, Riccardo Number Theory Algebraic Geometry 11G40, 11G50, 14K05, 11F67 We propose an investigation on the Northcott, Bogomolov and Lehmer properties for special values of L-functions. We first introduce an axiomatic approach to these three properties. We then focus on the Northcott property for special values of L-functions. In the case of L-functions of pure motives, we prove a Northcott property for special values located at the left of the critical strip, assuming that the L-functions in question satisfy some expected properties. Inside the critical strip, focusing on the Dedekind zeta function of number fields, we prove that such a property does not hold for the special value at one, but holds for the special value at zero, and we give a related quantitative estimate in this case. |
| title | On the Northcott property for special values of L-functions |
| topic | Number Theory Algebraic Geometry 11G40, 11G50, 14K05, 11F67 |
| url | https://arxiv.org/abs/2012.00542 |