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Topological Modular Forms [PDF]
, 2014 DEFINITION 3.5. An integral modular form of weight n is a law associating to every pointed curve of genus 1 a section of wo" in a way compatible with base change.
Douglas, C +3 more
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Journal of Number Theory, 2003 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Knopp, Marvin, Mason, Geoffrey
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Neutrino masses and mixing from double covering of finite modular groups
Journal of High Energy Physics, 2019 We extend the even weight modular forms of modular invariant approach to general integral weight modular forms. We find that the modular forms of integral weights and level N can be arranged into irreducible representations of the homogeneous finite ...
Xiang-Gan Liu, Gui-Jun Ding
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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
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Explicit construction of mock modular forms from weakly holomorphic Hecke eigenforms
Open Mathematics, 2022 Extending our previous work we construct weakly holomorphic Hecke eigenforms whose period polynomials correspond to elements in a basis consisting of odd and even Hecke eigenpolynomials induced by only cusp forms.
Choi SoYoung, Kim Chang Heon
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Modular Forms on Hecke's Modular Groups [PDF]
Proceedings of the American Mathematical Society, 1973 Let H={-r=x+iy:y>0}. Let A>0, k>O, y=I1. Let M(Q, k, y) denote the set of functions f for which f(r)= .D=o ane2'i"rli and f(-1/T)=y(&/i)kf(T), for all T r H. Let MO(A, k, y) denote the set of feM(A, k. y) for which f((T)=O(yc) uniformly for all x as y-+, for some real c.
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Shintani and Shimura lifts of cusp forms on certain arithmetic groups and their applications
Open Mathematics, 2017 For an odd and squarefree level N, Kohnen proved that there is a canonically defined subspace Sκ+12new(N)⊂Sκ+12(N),andSκ+12new(N)andS2knew(N)$S_{\kappa+\frac{1}{2}}^{\mathrm{n}\mathrm{e}\mathrm{w}}(N)\subset S_{\kappa+\frac{1}{2}}(N),\,\,{\text{and ...
Choi SoYoung, Kim Chang Heon
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, 2021 We examine several currently used techniques for visualizing complex-valued functions applied to modular forms. We plot several examples and study the benefits and limitations of each technique. We then introduce a method of visualization that can take advantage of colormaps in Python's matplotlib library, describe an implementation, and give 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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Modular invariant models of leptons at level 7
Journal of High Energy Physics, 2020 We consider for the first time level 7 modular invariant flavour models where the lepton mixing originates from the breaking of modular symmetry and couplings responsible for lepton masses are modular forms.
Gui-Jun Ding +3 more
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