Results 51 to 60 of about 162 (133)

A quadratic form with prime variables associated with Hecke eigenvalues of a cusp form

, 2022
summary:Let $f$ be a normalized primitive holomorphic cusp form of even integral weight $k$ for the full modular group ${\rm SL}(2,\mathbb {Z})$, and denote its $n$th Fourier coefficient by $\lambda _{f}(n)$.
Hua, Guodong
core   +1 more source

Integral Traces of Weak Maass Forms of Genus Zero Odd Prime Level

, 2013
Duke and Jenkins defined a family of linear maps from spaces of weakly holomorphic modular forms of negative integral weight and level 1 into spaces of weakly holomorphic modular forms of half integral weight and level 4 and showed that these lifts ...
Green, Nathan Eric
core  

A modular framework of functions of Knopp and indefinite binary quadratic forms

, 2022
In this paper, we investigate functions introduced by Knopp and complete them to non-holomorphic bimodular forms of positive integral weight related to indefinite binary quadratic forms.
Mono, Andreas, Bringmann, Kathrin
core  

Differential operators on polar harmonic Maass forms and elliptic duality

, 2019
In this paper, we study polar harmonic Maass forms of negative integral weight. Using work of Fay, we construct Poincaré series which span the space of such forms and show that their elliptic coefficients exhibit duality properties which are similar to ...
Jenkins, P, Bringmann, K, Bringmann, Kathrin, Jenkins, Paul, Kane, Ben, Kane, BR   +5 more
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Higher depth quantum modular forms, multiple Eichler integrals, and $\mathfrak{sl}_3$ false theta functions

, 2019
We introduce and study higher depth quantum modular forms. We construct two families of examples coming from rank two false theta functions, whose “companions” in the lower half-plane can be also realized both as double Eichler integrals and as non ...
Bringmann, K., Kaszian, Jonas, Milas, A., Bringmann, Kathrin, Kaszian, J., Milas, Antun   +5 more
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Modular knots, automorphic forms, and the Rademacher symbols for triangle groups. [PDF]

Res Math Sci, 2023
Matsusaka T, Ueki J.
europepmc   +1 more source

Construction of modular forms with Poincaré series

, 2010
Cataloged from PDF version of article.Includes bibliographical references leaves 63-65.In this thesis, we construct holomorphic modular forms of integral weight k > 2 for the principle congruence subgroup Γ( ¯ N) by means of Poincar´e series. We start by
Güneş, Çisem
core  

Modularity of generating series of winding numbers

, 2018
The Shimura correspondence connects modular forms of integral weights and half-integral weights. One of the directions is realized by the Shintani lift, where the inputs are holomorphic differentials and the outputs are holomorphic modular forms of half ...
Yingkun Li, Özlem Imamoḡlu, Funke, J., Li, Y., Jan H. Bruinier, Jens Funke, Bruinier, J., Imamoḡlu, Ö   +7 more
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Identities for traces of singular moduli [PDF]

, 2020
. Generalizing work of Zagier, in an important recent paper Bruinier and Funke prove that the generating functions for traces of singular values of many modular functions are weight 3 2 modular forms. Using facts about half-integral weight modular forms,
Kathrin Bringmann, Ken Ono
core  

TWISTED BORCHERDS PRODUCTS ON HILBERT MODULAR SURFACES AND THE REGULARIZED THETA LIFT

, 2010
We construct a lifting from weakly holomorphic modular forms of weight 0 for SL 2(ℤ) with integral Fourier coefficients to meromorphic Hilbert modular forms of weight 0 for the full Hilbert modular group of a real quadratic number field with an infinite
STEPHAN EHLEN
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