Modular forms of half-integral weight on Gamma(0)(4) with few nonvanishing coefficients modulo lopen access
- Authors
- Choi, Dohoon; Lee, Youngmin
- Issue Date
- 28-10월-2022
- Publisher
- DE GRUYTER POLAND SP Z O O
- Keywords
- Fourier coefficients of modular forms; Galois representations; modular forms of half-integral weight; theta functions
- Citation
- OPEN MATHEMATICS, v.20, no.1, pp.1320 - 1336
- Indexed
- SCIE
SCOPUS
- Journal Title
- OPEN MATHEMATICS
- Volume
- 20
- Number
- 1
- Start Page
- 1320
- End Page
- 1336
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/146536
- DOI
- 10.1515/math-2022-0512
- ISSN
- 2391-5455
- Abstract
- Let k be a nonnegative integer. Let K be a number field and O-K be the ring of integers of K. Let l >= 5 be a prime and v be a prime ideal of O-K over l. Let f be a modular form of weight k + 1/2 on Gamma(0)(4) such that its Fourier coefficients are in O-K. In this article, we study sufficient conditions that if f has the form f(z) Xi Sigma(infinity)(n=1)Sigma(t)(j=1) af(s(i)n(2))q(i)(s)n2 (mod v) with square-free integers s(i), then f is congruent to a linear combination of iterated derivatives of a single theta function modulo v.
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