Identities for Anderson generating functions for Drinfeld modules

Ahmad ElGuindy, Matthew A. Papanikolas

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

Anderson generating functions are generating series for division values of points on Drinfeld modules, and they serve as important tools for capturing periods, quasi-periods, and logarithms. They have been fundamental in recent work on special values of positive characteristic L-series and in transcendence and algebraic independence problems. In the present paper we investigate techniques for expressing Anderson generating functions in terms of the defining polynomial of the Drinfeld module and determine new formulas for periods and quasi-periods.

Original languageEnglish
Pages (from-to)471-493
Number of pages23
JournalMonatshefte fur Mathematik
Volume173
Issue number4
DOIs
Publication statusPublished - 2014

Fingerprint

Drinfeld Modules
Generating Function
Algebraic Independence
Transcendence
Series
Positive Characteristic
Logarithm
Division
Polynomial

Keywords

  • Anderson generating functions
  • Drinfeld logarithms
  • Drinfeld modules
  • periods
  • quasi-periods
  • shadowed partitions

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Identities for Anderson generating functions for Drinfeld modules. / ElGuindy, Ahmad; Papanikolas, Matthew A.

In: Monatshefte fur Mathematik, Vol. 173, No. 4, 2014, p. 471-493.

Research output: Contribution to journalArticle

ElGuindy, Ahmad ; Papanikolas, Matthew A. / Identities for Anderson generating functions for Drinfeld modules. In: Monatshefte fur Mathematik. 2014 ; Vol. 173, No. 4. pp. 471-493.
@article{dec37ad12497432196c70916683aa462,
title = "Identities for Anderson generating functions for Drinfeld modules",
abstract = "Anderson generating functions are generating series for division values of points on Drinfeld modules, and they serve as important tools for capturing periods, quasi-periods, and logarithms. They have been fundamental in recent work on special values of positive characteristic L-series and in transcendence and algebraic independence problems. In the present paper we investigate techniques for expressing Anderson generating functions in terms of the defining polynomial of the Drinfeld module and determine new formulas for periods and quasi-periods.",
keywords = "Anderson generating functions, Drinfeld logarithms, Drinfeld modules, periods, quasi-periods, shadowed partitions",
author = "Ahmad ElGuindy and Papanikolas, {Matthew A.}",
year = "2014",
doi = "10.1007/s00605-013-0543-9",
language = "English",
volume = "173",
pages = "471--493",
journal = "Monatshefte fur Mathematik",
issn = "0026-9255",
publisher = "Springer Wien",
number = "4",

}

TY - JOUR

T1 - Identities for Anderson generating functions for Drinfeld modules

AU - ElGuindy, Ahmad

AU - Papanikolas, Matthew A.

PY - 2014

Y1 - 2014

N2 - Anderson generating functions are generating series for division values of points on Drinfeld modules, and they serve as important tools for capturing periods, quasi-periods, and logarithms. They have been fundamental in recent work on special values of positive characteristic L-series and in transcendence and algebraic independence problems. In the present paper we investigate techniques for expressing Anderson generating functions in terms of the defining polynomial of the Drinfeld module and determine new formulas for periods and quasi-periods.

AB - Anderson generating functions are generating series for division values of points on Drinfeld modules, and they serve as important tools for capturing periods, quasi-periods, and logarithms. They have been fundamental in recent work on special values of positive characteristic L-series and in transcendence and algebraic independence problems. In the present paper we investigate techniques for expressing Anderson generating functions in terms of the defining polynomial of the Drinfeld module and determine new formulas for periods and quasi-periods.

KW - Anderson generating functions

KW - Drinfeld logarithms

KW - Drinfeld modules

KW - periods

KW - quasi-periods

KW - shadowed partitions

UR - http://www.scopus.com/inward/record.url?scp=84896392259&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84896392259&partnerID=8YFLogxK

U2 - 10.1007/s00605-013-0543-9

DO - 10.1007/s00605-013-0543-9

M3 - Article

VL - 173

SP - 471

EP - 493

JO - Monatshefte fur Mathematik

JF - Monatshefte fur Mathematik

SN - 0026-9255

IS - 4

ER -