Modular invariant of rank 1 Drinfeld modules and class field generation

L. Demangos; T. M. Gendron

doi:10.1016/j.jnt.2020.11.005

Modular invariant of rank 1 Drinfeld modules and class field generation

L. Demangos, T. M. Gendron^*

^*Corresponding author for this work

Department of Pure Mathematics

Universidad Nacional Autónoma de México

Research output: Contribution to journal › Article › peer-review

Abstract

The modular invariant of rank 1 Drinfeld modules is introduced and used to prove an exact analog of the Weber-Fueter theorem for global function fields. The main ingredient in the proof is the global function field version of Shimura's Main Theorem of Complex Multiplication.

Original language	English
Pages (from-to)	40-66
Number of pages	27
Journal	Journal of Number Theory
Volume	237
DOIs	https://doi.org/10.1016/j.jnt.2020.11.005
Publication status	Published - Aug 2022

Keywords

Explicit class field theory
Global function fields
Modular invariant

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10.1016/j.jnt.2020.11.005

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title = "Modular invariant of rank 1 Drinfeld modules and class field generation",

abstract = "The modular invariant of rank 1 Drinfeld modules is introduced and used to prove an exact analog of the Weber-Fueter theorem for global function fields. The main ingredient in the proof is the global function field version of Shimura's Main Theorem of Complex Multiplication.",

keywords = "Explicit class field theory, Global function fields, Modular invariant",

author = "L. Demangos and Gendron, {T. M.}",

note = "Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",

year = "2022",

month = aug,

doi = "10.1016/j.jnt.2020.11.005",

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AU - Demangos, L.

AU - Gendron, T. M.

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N2 - The modular invariant of rank 1 Drinfeld modules is introduced and used to prove an exact analog of the Weber-Fueter theorem for global function fields. The main ingredient in the proof is the global function field version of Shimura's Main Theorem of Complex Multiplication.

AB - The modular invariant of rank 1 Drinfeld modules is introduced and used to prove an exact analog of the Weber-Fueter theorem for global function fields. The main ingredient in the proof is the global function field version of Shimura's Main Theorem of Complex Multiplication.

KW - Explicit class field theory

KW - Global function fields

KW - Modular invariant

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SN - 0022-314X

VL - 237

SP - 40

EP - 66

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

Modular invariant of rank 1 Drinfeld modules and class field generation

Abstract

Keywords

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