| Full text | |
| Author(s): |
Grishkov, A.
;
Logachev, D.
;
Zobnin, A.
Total Authors: 3
|
| Document type: | Journal article |
| Source: | JOURNAL OF NUMBER THEORY; v. 238, p. 44-pg., 2022-05-26. |
| Abstract | |
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) | |
| FAPESP's process: | 17/19777-6 - Anderson t-motives, their L-functions and lattices |
| Grantee: | Alexandre Grichkov |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - Brazil |