|322 TMCB |
Department of Mathematics
Brigham Young University
Provo, UT 84602
p-adic properties of coefficients of weakly holomorphic modular forms
Abstract: We examine the Fourier coefficients of modular forms in a canonical basis for the space of weakly holomorphic modular forms of weights 4, 6, 8, 10, and 14, and show that these coefficients are often highly divisible by the primes 2, 3, and 5.
- Darrin Doud, Paul Jenkins and John Lopez, Two-divisibility of coefficients of certain weakly holomorphic modular forms, Ramanujan Journal, 28, (2012), 89-111.
- Soyoung Choi, p-adic properties of coefficients of basis for the space of weakly holomorphic modular forms of weight 2, Proc. Japan Acad., Ser. A 88, (2012), 11-15.
- Nickolas Andersen and Paul Jenkins, Divisibility properties of coefficients of level p modular functions for genus zero primes, Proc. AMS, 141 (2013), 41-53.
- Soyoung Choi and Chang Heon Kim, Basis for the space of weakly holomorphic modular forms in higher level cases, J. Number Theory, 133 (2013), 1300-1311.
- Sharon Anne Garthwaite and Paul Jenkins, Zeros of weakly holomorphic modular forms of levels 2 and 3, Math. Res. Lett., 20 (2013), 657-674.
- Paul Jenkins and D. J. Thornton, Congruences for coefficients of modular functions, Ramanujan J. 38 (2015), 619-628.
- Seiichi Hanamoto, Three-divisibility of Fourier coefficients of weakly holomorphic modular forms, Ramanujan J., 39 (2016), 117-132.