Independence between coefficients of two modular forms
- Authors
- Choi, Dohoon; Lim, Subong
- Issue Date
- 9월-2019
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Keywords
- Fourier coefficient; Modular form; Galois representation
- Citation
- JOURNAL OF NUMBER THEORY, v.202, pp.298 - 315
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF NUMBER THEORY
- Volume
- 202
- Start Page
- 298
- End Page
- 315
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/63446
- DOI
- 10.1016/j.jnt.2019.01.005
- ISSN
- 0022-314X
- Abstract
- Let k be an even integer and Sk be the space of cusp forms of weight k on SL2(Z). Let S = circle plus S-k is an element of 2z(k). For f, g is an element of S, we let R(f, g) be the set of ratios of the Fourier coefficients of f and g defined by R(f, g) := {x is an element of P-1 (C) vertical bar x = [a(f)(p) : a(g) (p)] for some prime p}, where a(f)(n) (resp. a(g)(n)) denotes the nth Fourier coefficient of f (resp. g). In this paper, we prove that if f and g are nonzero and R(f, g) is finite, then f = cg for some constant c. This result is extended to the space of weakly holomorphic modular forms on SL2(Z). We apply it to study the number of representations of a positive integer by a quadratic form. (C) 2019 Elsevier Inc. All rights reserved.
- Files in This Item
- There are no files associated with this item.
- Appears in
Collections - College of Science > Department of Mathematics > 1. Journal Articles
Items in ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.