The transcendence of zeros of canonical basis elements of the space of weakly holomorphic modular forms for Gamma(0)(2)

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We consider the canonical basis elements f(k,m)(epsilon) for the space of weakly holomorphic modular forms of weight k for the Hecke congruence group Gamma(0)(2) and we prove that for all m >= c(k) for some constant c(k), if z(0) in a fundamen- tal domain for Gamma(0)(2) is a zero of f(k,m)(epsilon), then either z(0) is in {i/root 2, - 1/2 + i/2, 1/2 + i/2, -1+i root 7/4, 1+i root 7/4} or z(0) is transcendental. (C) 2019 Elsevier Inc. All rights reserved.
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2019-11
Language
English
Article Type
Article
Citation

JOURNAL OF NUMBER THEORY, v.204, pp.423 - 434

ISSN
0022-314X
DOI
10.1016/j.jnt.2019.04.012
URI
http://hdl.handle.net/10203/264323
Appears in Collection
MA-Journal Papers(저널논문)
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