Lehmer problem and Drinfeld modules

Luca Demangos

doi:10.1016/j.jnt.2017.12.002

Lehmer problem and Drinfeld modules

Luca Demangos

Stellenbosch University

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

1 Citation (Scopus)

Abstract

We propose a lower bound estimate in Dobrowolski's form of the canonical height of a Drinfeld module having a positive density of supersingular primes. This estimate takes into account the inseparable case and it is given as a function of: the degree of the field of coefficients, the height of the module and its rank. We will show that the class of Drinfeld modules we consider includes all CM Drinfeld modules with rank either 1 or a prime number different from the field characteristic.

Original language	English
Pages (from-to)	147-185
Number of pages	39
Journal	Journal of Number Theory
Volume	189
DOIs	https://doi.org/10.1016/j.jnt.2017.12.002
Publication status	Published - Aug 2018
Externally published	Yes

Keywords

Complex multiplication
Drinfeld modules
Height theory
Lehmer problem

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10.1016/j.jnt.2017.12.002

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abstract = "We propose a lower bound estimate in Dobrowolski's form of the canonical height of a Drinfeld module having a positive density of supersingular primes. This estimate takes into account the inseparable case and it is given as a function of: the degree of the field of coefficients, the height of the module and its rank. We will show that the class of Drinfeld modules we consider includes all CM Drinfeld modules with rank either 1 or a prime number different from the field characteristic.",

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AB - We propose a lower bound estimate in Dobrowolski's form of the canonical height of a Drinfeld module having a positive density of supersingular primes. This estimate takes into account the inseparable case and it is given as a function of: the degree of the field of coefficients, the height of the module and its rank. We will show that the class of Drinfeld modules we consider includes all CM Drinfeld modules with rank either 1 or a prime number different from the field characteristic.

KW - Complex multiplication

KW - Drinfeld modules

KW - Height theory

KW - Lehmer problem

UR - https://www.scopus.com/pages/publications/85040797617

U2 - 10.1016/j.jnt.2017.12.002

DO - 10.1016/j.jnt.2017.12.002

M3 - Article

AN - SCOPUS:85040797617

SN - 0022-314X

VL - 189

SP - 147

EP - 185

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

Lehmer problem and Drinfeld modules

Abstract

Keywords

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