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- Title
CLASSIFICATION OF CONGRUENCES FOR MOCK THETA FUNCTIONS AND WEAKLY HOLOMORPHIC MODULAR FORMS.
- Authors
Andersen, Nickolas
- Abstract
Let ƒ(q) denote Ramanujan's mock theta function. ƒ(q) = ∑a(n)qn:= 1 + ∑... It is known that there are many linear congruences for the coefficients of ƒ(q) and other mock theta functions. We prove that if the linear congruence a(mn+t) ≡ 0 (mod ℓ) holds for some prime ℓ ≥ 5, then ℓ|m and ((24t − 1)/ℓ) ≠ (−1/ℓ). We prove analogous results for the mock theta function ω(q) and for a large class of weakly holomorphic modular forms which includes η-quotients. This extends work of Radu, in which he proves a conjecture of Ahlgren and Ono for the partition function p(n).
- Subjects
GEOMETRIC congruences; THETA functions; HOLOMORPHIC functions; MODULAR forms; PARTITION functions
- Publication
Quarterly Journal of Mathematics, 2014, Vol 65, Issue 3, p781
- ISSN
0033-5606
- Publication type
Article
- DOI
10.1093/qmath/hat051