Resultantal varieties related to zeroes of L-functions of Carlitz modules

Autor(es)

Grishkov, A. ^[1] ; Logachev, D. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Dept Matemat & Estat, BR-05508 Sao Paulo - Brazil

^[2] Univ Fed Amazonas, ICE, DM, Manaus, Amazonas - Brazil

• Tipo de documento: Artigo Científico
• Fonte: FINITE FIELDS AND THEIR APPLICATIONS; v. 38, p. 116-176, MAR 2016.
• Citações Web of Science: 1

Resumo

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 relevant polynomial determinant. (C) 2015 Published by Elsevier Inc. (AU)

• Processo FAPESP: 13/10596-8 - Loopos algébricos e módulos de Drinfeld
• Beneficiário: Alexandre Grichkov
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional