Poincaré series and the divisors of modular forms

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

Recently, Bruinier, Kohnen and Ono obtained an explicit description of the action of the theta-operator on meromorphic modular forms f on SL 2(ℤ) in terms of the values of modular functions at points in the divisor of f. Using this result, they studied the exponents in the infinite product expansion of a modular form and recurrence relations for Fourier coefficients of a modular form. In this paper, we extend these results to meromorphic modular forms on Γ0(N) for an arbitrary positive integer N >1.

Original languageEnglish
Pages (from-to)3393-3403
Number of pages11
JournalProceedings of the American Mathematical Society
Volume138
Issue number10
DOIs
Publication statusPublished - 2010 Oct 1
Externally publishedYes

Fingerprint

Modular Forms
Divisor
Series
Meromorphic
Modular Functions
Infinite product
Fourier coefficients
Recurrence relation
Exponent
Integer
Arbitrary
Operator

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Poincaré series and the divisors of modular forms. / Choi, Dohoon.

In: Proceedings of the American Mathematical Society, Vol. 138, No. 10, 01.10.2010, p. 3393-3403.

Research output: Contribution to journalArticle

@article{7140aa041fb54d6c976782284a156851,
title = "Poincar{\'e} series and the divisors of modular forms",
abstract = "Recently, Bruinier, Kohnen and Ono obtained an explicit description of the action of the theta-operator on meromorphic modular forms f on SL 2(ℤ) in terms of the values of modular functions at points in the divisor of f. Using this result, they studied the exponents in the infinite product expansion of a modular form and recurrence relations for Fourier coefficients of a modular form. In this paper, we extend these results to meromorphic modular forms on Γ0(N) for an arbitrary positive integer N >1.",
author = "Dohoon Choi",
year = "2010",
month = "10",
day = "1",
doi = "10.1090/S0002-9939-2010-10133-8",
language = "English",
volume = "138",
pages = "3393--3403",
journal = "Proceedings of the American Mathematical Society",
issn = "0002-9939",
publisher = "American Mathematical Society",
number = "10",

}

TY - JOUR

T1 - Poincaré series and the divisors of modular forms

AU - Choi, Dohoon

PY - 2010/10/1

Y1 - 2010/10/1

N2 - Recently, Bruinier, Kohnen and Ono obtained an explicit description of the action of the theta-operator on meromorphic modular forms f on SL 2(ℤ) in terms of the values of modular functions at points in the divisor of f. Using this result, they studied the exponents in the infinite product expansion of a modular form and recurrence relations for Fourier coefficients of a modular form. In this paper, we extend these results to meromorphic modular forms on Γ0(N) for an arbitrary positive integer N >1.

AB - Recently, Bruinier, Kohnen and Ono obtained an explicit description of the action of the theta-operator on meromorphic modular forms f on SL 2(ℤ) in terms of the values of modular functions at points in the divisor of f. Using this result, they studied the exponents in the infinite product expansion of a modular form and recurrence relations for Fourier coefficients of a modular form. In this paper, we extend these results to meromorphic modular forms on Γ0(N) for an arbitrary positive integer N >1.

UR - http://www.scopus.com/inward/record.url?scp=77955652416&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77955652416&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-2010-10133-8

DO - 10.1090/S0002-9939-2010-10133-8

M3 - Article

VL - 138

SP - 3393

EP - 3403

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 10

ER -