Explicit congruences for mock modular forms [PDF]
, 2015 In recent work of Bringmann, Guerzhoy, and the first author, p-adic modular forms were constructed from mock modular forms.
Kane, Ben, Waldherr, Matthias
core +2 more sources
ZAGIER DUALITY FOR HARMONIC WEAK MAASS FORMS OF INTEGRAL WEIGHT [PDF]
, 2010 We show the existence of "Zagier duality" between vector valued harmonic weak Maass forms and vector valued weakly holomorphic modular forms of integral weight.
Bumkyu Cho, Y. Choie
semanticscholar +1 more source
Locally harmonic Maass forms and the kernel of the Shintani lift [PDF]
, 2014 In this paper we define a new type of modular object and construct explicit examples of such functions. Our functions are closely related to cusp forms constructed by Zagier which played an important role in the construction by Kohnen and Zagier of a ...
Bringmann, Kathrin +2 more
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$p$-adic properties of coefficients of weakly holomorphic modular forms [PDF]
, 2009 We examine the Fourier coefficients of modular forms in a canonical basis for the spaces of weakly holomorphic modular forms of weights 4, 6, 8, 10, and 14, and show that these coefficients are often highly divisible by the primes 2, 3, and 5.Comment: 16
Doud, Darrin, Jenkins, Paul
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Topological Strings and (Almost) Modular Forms [PDF]
, 2006 The B-model topological string theory on a Calabi-Yau threefold X has a symmetry group Gamma, generated by monodromies of the periods of X. This acts on the topological string wave function in a natural way, governed by the quantum mechanics of the phase
A. Klemm +25 more
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Polar harmonic Maass forms and their applications [PDF]
, 2016 In this survey, we present recent results of the authors about non-meromorphic modular objects known as polar harmonic Maass forms. These include the computation of Fourier coefficients of meromorphic modular forms and relations between inner products of
Bringmann, Kathrin, Kane, Ben
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Heterotic-string amplitudes at one loop: modular graph forms and relations to open strings [PDF]
, 2019 We investigate one-loop four-point scattering of non-abelian gauge bosons in heterotic string theory and identify new connections with the corresponding open-string amplitude.
Gerken, Jan E. +2 more
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Petersson inner products of weight-one modular forms [PDF]
Journal für die Reine und Angewandte Mathematik, 2012 In this paper we study the regularized Petersson product between a holomorphic theta series associated to a positive definite binary quadratic form and a weakly holomorphic weight-one modular form with integral Fourier coefficients.
M. Viazovska
semanticscholar +1 more source
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
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Higher depth quantum modular forms, multiple Eichler integrals, and $$\mathfrak {sl}_3$$sl3 false theta functions [PDF]
Research in the Mathematical Sciences, 2017 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 ...
K. Bringmann, Jonas Kaszian, A. Milas
semanticscholar +1 more source