Coefficients of half-integral weight modular forms modulo ?j

Ahlgren, Scott; Boylan, Matthew

doi:10.1007/s00208-004-0555-9

Cited by 17 publications

(43 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…So, our following theorem is an analog of the result of Ahlgren and Boylan (Theorem 2 in [2]) for weakly holomorphic modular forms of half-integral weight such that the constant terms of their q-expansions are not zero modulo .…”

Section: Theorem (Theorem 2 In [2]) Suppose That We Have the Followimentioning

confidence: 80%

“…In [2] Ahlgren and Boylan proved that if f (z) is a modular form whose coefficients are supported on finitely many square classes modulo , then, as predicted by Conjecture A, the values of λ are restricted.…”

Section: Conjecture a (Conjecture A In [5]) Suppose That λ Is A Nonnmentioning

confidence: 99%

“…Our argument for the proof of Theorem 2 is based on the work of Bruinier and Ono [7] and of Ahlgren and Boylan [1], [3], [4].…”

Section: Lemma 33 Suppose That λ Is a Nonnegative Integer That N Imentioning

confidence: 99%

“…When the weight is half-integral, the situation is not as clear. The distribution of the coefficients of modular forms of half-integral weight in congruence classes has been studied by, among others, Balog, Darmon, and Ono [5], Ono and Skinner [14], [15], Brunier [6], Bruinier and Ono [7], and Ahlgren and Boylan [1], [2]. In this paper, we study congruences for weakly holomorphic modular forms of half-integral weight such that the constant terms of their q-expansions are not zero modulo a prime .…”

Section: Introductionmentioning

confidence: 99%

“…S λ+ 1 2 (Γ 0 (N ), χ)). Let M λ+ 1 2 (Γ 0 (N )) be the space of weakly holomorphic modular forms of weight λ + Recently it was proved in [7] and [2] that…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Weakly holomorphic modular forms of half-integral weight with nonvanishing constant terms modulo $\ell $

Choi

2009

Trans. Amer. Math. Soc.

View full text Add to dashboard Cite

Abstract. Let be a prime and λ, j ≥ 0 be an integer. Suppose that f (z) = n a(n)q n is a weakly holomorphic modular form of weight λ + 1 2and that a(0) ≡ 0 (mod ). We prove that if the coefficients of f (z) are not "welldistributed" modulo j , thenThis implies that, under the additional restriction a(0) ≡ 0 (mod ), the following conjecture of Balog, Darmon and Ono is true: if the coefficients of a modular form of weight λ+ 1 2 are almost (but not all) divisible by , then either λ ≡ 0 (mod). We also prove that if λ ≡ 0 and 1 (mod −1 2 ), then there does not exist an integer β, 0 ≤ β < , such that a( n + β) ≡ 0 (mod ) for every nonnegative integer n. As an application, we study congruences for the values of the overpartition function.

show abstract

Section: Theorem (Theorem 2 In [2]) Suppose That We Have the Followimentioning

confidence: 80%

Section: Conjecture a (Conjecture A In [5]) Suppose That λ Is A Nonnmentioning

confidence: 99%

“…Our argument for the proof of Theorem 2 is based on the work of Bruinier and Ono [7] and of Ahlgren and Boylan [1], [3], [4].…”

Section: Lemma 33 Suppose That λ Is a Nonnegative Integer That N Imentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…S λ+ 1 2 (Γ 0 (N ), χ)). Let M λ+ 1 2 (Γ 0 (N )) be the space of weakly holomorphic modular forms of weight λ + Recently it was proved in [7] and [2] that…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations