On certain coefficients of Drinfeld-Goss eigenforms with power eigenvalues

Ahmad ElGuindy, Aleksandar Petrov

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We show that a certain family of the coefficients of a Drinfeld-Goss modular form with certain power eigenvalues for the Hecke operators at degree 1 primes the can be expressed as polynomial multiples of the first possible non-zero coefficient of that form. Along the way, we obtain some interesting combinatorial properties regarding difference operators in finite characteristic.

Original languageEnglish
Article number10
JournalResearch in Number Theory
Volume2
Issue number1
DOIs
Publication statusPublished - 1 Dec 2016

Fingerprint

Eigenvalue
Hecke Operators
Difference Operator
Modular Forms
Coefficient
Polynomial
Form
Family

Keywords

  • Difference operators
  • Drinfeld-Goss modular forms
  • Eigenform coefficients
  • Hecke operators

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

On certain coefficients of Drinfeld-Goss eigenforms with power eigenvalues. / ElGuindy, Ahmad; Petrov, Aleksandar.

In: Research in Number Theory, Vol. 2, No. 1, 10, 01.12.2016.

Research output: Contribution to journalArticle

@article{eb13153ad82840dab95a6ba886bdfc52,
title = "On certain coefficients of Drinfeld-Goss eigenforms with power eigenvalues",
abstract = "We show that a certain family of the coefficients of a Drinfeld-Goss modular form with certain power eigenvalues for the Hecke operators at degree 1 primes the can be expressed as polynomial multiples of the first possible non-zero coefficient of that form. Along the way, we obtain some interesting combinatorial properties regarding difference operators in finite characteristic.",
keywords = "Difference operators, Drinfeld-Goss modular forms, Eigenform coefficients, Hecke operators",
author = "Ahmad ElGuindy and Aleksandar Petrov",
year = "2016",
month = "12",
day = "1",
doi = "10.1007/s40993-015-0034-2",
language = "English",
volume = "2",
journal = "Research in Number Theory",
issn = "2363-9555",
publisher = "Springer Open",
number = "1",

}

TY - JOUR

T1 - On certain coefficients of Drinfeld-Goss eigenforms with power eigenvalues

AU - ElGuindy, Ahmad

AU - Petrov, Aleksandar

PY - 2016/12/1

Y1 - 2016/12/1

N2 - We show that a certain family of the coefficients of a Drinfeld-Goss modular form with certain power eigenvalues for the Hecke operators at degree 1 primes the can be expressed as polynomial multiples of the first possible non-zero coefficient of that form. Along the way, we obtain some interesting combinatorial properties regarding difference operators in finite characteristic.

AB - We show that a certain family of the coefficients of a Drinfeld-Goss modular form with certain power eigenvalues for the Hecke operators at degree 1 primes the can be expressed as polynomial multiples of the first possible non-zero coefficient of that form. Along the way, we obtain some interesting combinatorial properties regarding difference operators in finite characteristic.

KW - Difference operators

KW - Drinfeld-Goss modular forms

KW - Eigenform coefficients

KW - Hecke operators

UR - http://www.scopus.com/inward/record.url?scp=85019992008&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85019992008&partnerID=8YFLogxK

U2 - 10.1007/s40993-015-0034-2

DO - 10.1007/s40993-015-0034-2

M3 - Article

VL - 2

JO - Research in Number Theory

JF - Research in Number Theory

SN - 2363-9555

IS - 1

M1 - 10

ER -