Explicit formulas for Drinfeld modules and their periods

Ahmad ElGuindy, Matthew A. Papanikolas

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We provide explicit series expansions for the exponential and logarithm functions attached to a rank r Drinfeld module that generalize well-known formulas for the Carlitz exponential and logarithm. Using these results we obtain a procedure and an analytic expression for computing the periods of rank 2 Drinfeld modules and also a criterion for supersingularity.

Original languageEnglish
Pages (from-to)1864-1886
Number of pages23
JournalJournal of Number Theory
Volume133
Issue number6
DOIs
Publication statusPublished - Jun 2013

Fingerprint

Drinfeld Modules
Logarithm
Explicit Formula
Series Expansion
Generalise
Computing

Keywords

  • Drinfeld modules
  • Exponentials
  • Logarithms
  • Periods
  • Supersingularity

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Explicit formulas for Drinfeld modules and their periods. / ElGuindy, Ahmad; Papanikolas, Matthew A.

In: Journal of Number Theory, Vol. 133, No. 6, 06.2013, p. 1864-1886.

Research output: Contribution to journalArticle

ElGuindy, Ahmad ; Papanikolas, Matthew A. / Explicit formulas for Drinfeld modules and their periods. In: Journal of Number Theory. 2013 ; Vol. 133, No. 6. pp. 1864-1886.
@article{f535186aa406458e899cd21320171428,
title = "Explicit formulas for Drinfeld modules and their periods",
abstract = "We provide explicit series expansions for the exponential and logarithm functions attached to a rank r Drinfeld module that generalize well-known formulas for the Carlitz exponential and logarithm. Using these results we obtain a procedure and an analytic expression for computing the periods of rank 2 Drinfeld modules and also a criterion for supersingularity.",
keywords = "Drinfeld modules, Exponentials, Logarithms, Periods, Supersingularity",
author = "Ahmad ElGuindy and Papanikolas, {Matthew A.}",
year = "2013",
month = "6",
doi = "10.1016/j.jnt.2012.10.013",
language = "English",
volume = "133",
pages = "1864--1886",
journal = "Journal of Number Theory",
issn = "0022-314X",
publisher = "Academic Press Inc.",
number = "6",

}

TY - JOUR

T1 - Explicit formulas for Drinfeld modules and their periods

AU - ElGuindy, Ahmad

AU - Papanikolas, Matthew A.

PY - 2013/6

Y1 - 2013/6

N2 - We provide explicit series expansions for the exponential and logarithm functions attached to a rank r Drinfeld module that generalize well-known formulas for the Carlitz exponential and logarithm. Using these results we obtain a procedure and an analytic expression for computing the periods of rank 2 Drinfeld modules and also a criterion for supersingularity.

AB - We provide explicit series expansions for the exponential and logarithm functions attached to a rank r Drinfeld module that generalize well-known formulas for the Carlitz exponential and logarithm. Using these results we obtain a procedure and an analytic expression for computing the periods of rank 2 Drinfeld modules and also a criterion for supersingularity.

KW - Drinfeld modules

KW - Exponentials

KW - Logarithms

KW - Periods

KW - Supersingularity

UR - http://www.scopus.com/inward/record.url?scp=84872394317&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84872394317&partnerID=8YFLogxK

U2 - 10.1016/j.jnt.2012.10.013

DO - 10.1016/j.jnt.2012.10.013

M3 - Article

VL - 133

SP - 1864

EP - 1886

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

IS - 6

ER -