| Texto completo | |
| Autor(es): |
Grishkov, A.
;
Logachev, D.
;
Zobnin, A.
Número total de Autores: 3
|
| Tipo de documento: | Artigo Científico |
| Fonte: | JOURNAL OF NUMBER THEORY; v. 238, p. 44-pg., 2022-05-26. |
| Resumo | |
We continue study of some algebraic varieties (called resultantal varieties) started in a paper of A. Grishkov, D. Logachev "Resultantal varieties related to zeroes of L-functions of Carlitz modules". These varieties are related with the Sylvester matrix for the resultant of two polynomials, from one side, and with the L-functions of twisted Carlitz modules, from another side. Surprisingly, these varieties are described in terms of finite weighted rooted binary trees. We give a (conjecturally) complete description of them, we find parametrizations of their irreducible components and their invariants: degrees, multiplicities, Jordan forms, Galois actions. Proof of the fact that this description is really complete is a subject of future research. Maybe a generalization of these results will give us a solution of the problem of boundedness of the analytic rank of twists of Carlitz modules. (C) 2021 Elsevier Inc. All rights reserved. (AU) | |
| Processo FAPESP: | 17/19777-6 - T-motivos de Anderson, seus L-funções e reticulados |
| Beneficiário: | Alexandre Grichkov |
| Modalidade de apoio: | Auxílio à Pesquisa - Pesquisador Visitante - Brasil |