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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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Double cover of modular S4 for flavour model building
Nuclear Physics B, 2021 We develop the formalism of the finite modular group Γ4′≡S4′, a double cover of the modular permutation group Γ4≃S4, for theories of flavour. The integer weight k>0 of the level 4 modular forms indispensable for the formalism can be even or odd.
P.P. Novichkov, J.T. Penedo, S.T. Petcov
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Counting Curves with Modular Forms [PDF]
, 1996 We consider the type IIA string compactified on the Calabi-Yau space given by a degree 12 hypersurface in the weighted projective space ${\bf P}^4_{(1, 1, 2,2, 6)}$.
Antoniadis +16 more
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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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Poincaré series for modular graph forms at depth two. Part I. Seeds and Laplace systems
Journal of High Energy Physics, 2022 We derive new Poincaré-series representations for infinite families of non-holomorphic modular invariant functions that include modular graph forms as they appear in the low-energy expansion of closed-string scattering amplitudes at genus one.
Daniele Dorigoni +2 more
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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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Negative index Jacobi forms and quantum modular forms [PDF]
, 2014 In this paper, we consider the Fourier coefficients of a special class of meromorphic Jaocbi forms of negative index. Much recent work has been done on such coefficients in the case of Jacobi forms of positive index, but almost nothing is known for ...
Bringmann, Kathrin +2 more
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Coefficients of symmetric power L-functions on integers under digital constraints [PDF]
Notes on Number Theory and Discrete MathematicsLet λₛᵧₘʳ_f(n) be the n-th coefficient in the Dirichlet series representing the symmetric power L-function attached to a primitive form f of weight k and level N.
Khadija Mbarki
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