p-Adic limit of the Fourier coefficients of weakly holomorphic modular forms of half integral weight

Dohoon Choi, Y. Choie

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Serre obtained the p-adic limit of the integral Fourier coefficients of modular forms on SL2(ℤ) for p = 2,3,5,7. In this paper, we extend the result of Serre to weakly holomorphic modular forms of half integral weight on Γ0(4N) for N = 1,2,4. The proof is based on linear relations among Fourier coefficients of modular forms of half integral weight. As applications to our main result, we obtain congruences on various modular objects, such as those for Borcherds exponents, for Fourier coefficients of quotients of Eisentein series and for Fourier coefficients of Siegel modular forms on the Maass Space.

Original languageEnglish
Pages (from-to)61-83
Number of pages23
JournalIsrael Journal of Mathematics
Volume175
Issue number1
DOIs
Publication statusPublished - 2010 Jan 1
Externally publishedYes

Fingerprint

Modular Forms
Fourier coefficients
P-adic
Siegel Modular Forms
Linear Relation
Congruence
Quotient
Exponent
Series

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

p-Adic limit of the Fourier coefficients of weakly holomorphic modular forms of half integral weight. / Choi, Dohoon; Choie, Y.

In: Israel Journal of Mathematics, Vol. 175, No. 1, 01.01.2010, p. 61-83.

Research output: Contribution to journalArticle

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