Results 31 to 40 of about 6,496 (142)
Weakly holomorphic modular forms for some moonshine groups [PDF]
Archiv der Mathematik, 2014 In an article in the Pure and Applied Mathematics Quarterly in 2008, Duke and Jenkins investigated a certain natural basis of the space of weakly holomorphic modular forms for the full modular group $SL_2({\bf Z})$. We show here that their results can be generalized to certain moonshine groups, also allowing characters that are real on the underlying ...
Lahr, Martina, Schulze-Pillot, Rainer
openaire +2 more sources
Sign-Periodicity of Traces of Singular Moduli
Mathematics, 2013 Zagier proved that the generating functions of traces of singular values of Jm(z) are weight 3/2 weakly holomorphic modular forms. In this paper we prove that there is the sign-periodicity of traces of singular values of Jm(z).
Subong Lim, Dohoon Choi, Byungchan Kim
doaj +1 more source
Shintani lifts and fractional derivatives for harmonic weak Maass forms [PDF]
, 2014 In this paper, we construct Shintani lifts from integral weight weakly holomorphic modular forms to half-integral weight weakly holomorphic modular forms.
Bringmann, Kathrin +2 more
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Regularized inner products and weakly holomorphic Hecke eigenforms [PDF]
, 2017 We show that the image of repeated differentiation on weak cusp forms is precisely the subspace which is orthogonal to the space of weakly holomorphic modular forms.
Bringmann, Kathrin, Kane, Ben
core +2 more sources
Algebraic formulas for the coefficients of mock theta functions and Weyl vectors of Borcherds products [PDF]
, 2017 We present some applications of the Kudla-Millson and the Millson theta lift. The two lifts map weakly holomorphic modular functions to vector valued harmonic Maass forms of weight $3/2$ and $1/2$, respectively.
Bruinier, Jan Hendrik +1 more
core +1 more source
Linear relations between modular forms for Ğ“0+(p)
Open Mathematics, 2015 We find linear relations among the Fourier coefficients of modular forms for the group Ğ“0+(p) of genus zero. As an application of these linear relations, we derive congruence relations satisfied by the Fourier coefficients of normalized Hecke eigenforms.
Choi SoYoung, Kim Chang Heon
doaj +1 more source
On the algebraicity of coefficients of half-integral weight mock modular forms
Open Mathematics, 2018 Extending works of Ono and Boylan to the half-integral weight case, we relate the algebraicity of Fourier coefficients of half-integral weight mock modular forms to the vanishing of Fourier coefficients of their shadows.
Choi SoYoung, Kim Chang Heon
doaj +1 more source
Faber polynomials and poincare series [PDF]
, 2011 In this paper we consider weakly holomorphic modular forms (i.e., those meromorphic modular forms for which poles only possibly occur at the cusps) of weight 2−k∈2\Z for the full modular group \SL2(\Z).
Kane, B
core +2 more sources
Zeros of modular forms of half integral weight [PDF]
, 2016 We study canonical bases for spaces of weakly holomorphic modular forms of level 4 and weights in $\mathbb{Z}+\frac{1}{2}$ and show that almost all modular forms in these bases have the property that many of their zeros in a fundamental domain for ...
Folsom, Amanda, Jenkins, Paul
core +2 more sources
Open Mathematics, 2019 After the significant work of Zagier on the traces of singular moduli, Jeon, Kang and Kim showed that the Galois traces of real-valued class invariants given in terms of the singular values of the classical Weber functions can be identified with the ...
Eum Ick Sun, Jung Ho Yun
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