The transcendence of zeros of canonical basis elements of the space of weakly holomorphic modular forms for Γ0(2)

• Published in: Journal of number theory Vol. 204; pp. 423 - 434
• Main Authors: Choi, SoYoung, Im, Bo-Hae
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.11.2019
• Subjects: Weakly holomorphic modular form; 11F03; Weakly holomorphic modular form; 11F11
• ISSN: 0022-314X; 1096-1658
• DOI: 10.1016/j.jnt.2019.04.012

We consider the canonical basis elements fk,mε for the space of weakly holomorphic modular forms of weight k for the Hecke congruence group Γ0(2) and we prove that for all m≥c(k) for some constant c(k), if z0 in a fundamental domain for Γ0(2) is a zero of fk,mε, then either z0 is in {i2,−12+i2,12+i2,−1+i74,1+i74}, or z0 is transcendental.