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Working paper

L-functions of Carlitz modules, resultantal varieties and rooted binary trees

Logachev D., Aleksey Zobnin.
We continue study of varieties started in a paper of A. Grishkov, D. Logachev "Resultantal varieties related to zeroes of L-functions of Carlitz modules". We give a (conjecturally) complete description of these varieties in terms of rooted binary trees, we find parametrizations of their irreducible components and their invariants: degrees, multiplicities, Jordan forms, Galois actions. Maybe a generalization of this research will give us a solution of the problem of boundedness of the analytic rank of twists of Carlitz modules.