Resultantal varieties related to zeroes of L-functions of Carlitz modules
Abstract
We show that there exists a connection between two types of objects: some kind of resultantal varieties over C, from one side, and varieties of twists of the tensor powers of the Carlitz module such that the order of 0 of its L-functions at infinity is a constant, from another side. Obtained results are only a starting point of a general theory. We can expect that it will be possible to prove that the order of 0 of these L-functions at 1 (i.e. the analytic rank of a twist) is not bounded --- this is the function field case analog of the famous conjecture on non-boundedness of rank of twists of an elliptic curve over Q. The paper contains a calculation of a non-trivial polynomial determinant.
Keywords
Cite
@article{arxiv.1205.2900,
title = {Resultantal varieties related to zeroes of L-functions of Carlitz modules},
author = {Alexandr N. Grishkov and Dmitry Logachev},
journal= {arXiv preprint arXiv:1205.2900},
year = {2015}
}
Comments
53 pages; new result on calculation of a polynomial determinant is included