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L-functions of Carlitz modules, resultan...
Grishkov, Aleksandr...

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L-functions of Carlitz modules, resultantal varieties and rooted binary trees, II by Grishkov, Aleksandr ( Author )
Lemonjar Open Access
Australian National University
09-08-2023
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.
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Article
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29.34 KB
English
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MYR 0.01
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http://arxiv.org/abs/1607.06147
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