Results 21 to 30 of about 6,496 (142)
Divisibility properties for weakly holomorphic modular forms with sign vectors [PDF]
International Journal of Number Theory, 2016 In this paper, we prove some divisibility results for the Fourier coefficients of reduced modular forms with sign vectors. More precisely, we generalize a divisibility result of Siegel on constant terms when the weight [Formula: see text], which is related to the weight of Borcherds lifts when [Formula: see text].
Yichao Zhang
exaly +3 more sources
Basis for the space of weakly holomorphic modular forms in higher level cases
Journal of Number Theory, 2013 Let \(p\) be either \(1\) or a prime number. Let \(\Gamma_0(p)^+\) be the group generated by the group \(\Gamma_0(p)\) and the Fricke involution \(W_p\) and \(M_k^!(\Gamma_0(p)^+)\) be the space of weakly holomorphic modular forms (that is, meromorphic with poles only at the cusps) of even integral weight \(k\) with respect to \(\Gamma_0(p)^+\).
Soyoung Choi, Chang Heon Kim
semanticscholar +5 more sources
Mock theta functions and weakly holomorphic modular forms modulo 2 and 3 [PDF]
Mathematical Proceedings of the Cambridge Philosophical Society, 2013 We prove that the coefficients of certain mock theta functions possess no linear congruences modulo 3. We prove similar results for the moduli 2 and 3 for a wide class of weakly holomorphic modular forms and discuss applications.
Ahlgren, Scott, Kim, Byungchan
core +4 more sources
Two-divisibility of the coefficients of certain weakly holomorphic modular forms [PDF]
The Ramanujan Journal, 2011 We study a canonical basis for spaces of weakly holomorphic modular forms of weights 12, 16, 18, 20, 22, and 26 on the full modular group. We prove a relation between the Fourier coefficients of modular forms in this canonical basis and a generalized ...
A. El-Guindy +18 more
core +2 more sources
Classification of congruences for mock theta functions and weakly holomorphic modular forms [PDF]
The Quarterly Journal of Mathematics, 2013 Let $f(q)$ denote Ramanujan's mock theta function \[f(q) = \sum_{n=0}^{\infty} a(n) q^{n} := 1+\sum_{n=1}^{\infty} \frac{q^{n^{2}}}{(1+q)^{2}(1+q^{2})^{2}\cdots(1+q^{n})^{2}}.\] It is known that there are many linear congruences for the coefficients of ...
Nickolas Andersen
semanticscholar +4 more sources
Zagier duality and integrality of Fourier coefficients for weakly holomorphic modular forms
Journal of Number Theory, 2015 Worked out the isomorphisms for a general sign vector; proved Zagier duality for canonical bases; raise a question on integrality; 24 ...
Yichao Zhang
exaly +3 more sources
Weakly holomorphic modular forms in prime power levels of genus zero
, 2017 Let $M_k^\sharp(N)$ be the space of weight $k$, level $N$ weakly holomorphic modular forms with poles only at the cusp at $\infty$. We explicitly construct a canonical basis for $M_k^\sharp(N)$ for $N\in\{8,9,16,25\}$, and show that many of the Fourier ...
Da Silva, Caroline M. +3 more
core +3 more sources
Special L -values and periods of weakly holomorphic modular forms [PDF]
Proceedings of the American Mathematical Society, 2014 The authors study the special values of \(L\)-functions associated to weakly holomorphic modular forms; to define such an \(L\)-function, one makes use of appropriate regularization procedures. Let us cite a few of the authors': for \(f\in S^!_k\), where \(S^!_k\) denotes the space of weight \(k\) weakly holomorphic cusp forms, write \[ f(z)= \sum ...
K. Bringmann, K. Fricke, Zachary A. Kent
semanticscholar +4 more sources
Odd coefficients of weakly holomorphic modular forms [PDF]
Mathematical Research Letters, 2008 ). We will consider the question ofestimating the number of integers n for which a(n) 6≡0 (mod v).For a well-studied example, let p(n) be the ordinary partition function. Manyauthors have considered the problem of estimating the number of odd values of p(n).Among other references, one may see [1], [5], [15], [16], [17], [18], [19], [22], or [24].To see
Scott Ahlgren, Matthew Boylan
openaire +1 more source
Rank generating functions as weakly holomorphic modular forms [PDF]
Acta Arithmetica, 2008 We study infinite families of generating functions involving the rank of the ordinary partition function, which include as special cases many of the generating functions introduced by Atkin and Swinnerton-Dyer in the 1950s. We prove that each of these generating functions is a weakly holomorphic modular form of weight 1/2 on some congruence subgroup Γ1(
Scott Ahlgren, Stephanie Treneer
openaire +1 more source