Results 71 to 80 of about 378,592 (232)
American Journal of Mathematics, 2006 In this paper, we study modular forms on two simply connected groups of type D 4 over Q. One group, G s , is a globally split group of type D 4 , viewed as the group of isotopies of the split rational octonions. The other, G c , is the isotopy group of the rational (nonsplit) octonions. We study automorphic forms on G s in analogy to the work of Gross,
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New A 4 lepton flavor model from S 4 modular symmetry
Journal of High Energy Physics, 2020 We study a flavor model with A 4 symmetry which originates from S 4 modular group. In S 4 symmetry, Z 2 subgroup can be anomalous, and then S 4 can be violated to A 4.
Tatsuo Kobayashi +4 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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Plea for Diagonals and Telescopers of Rational Functions
UniverseThis paper is a plea for diagonals and telescopers of rational or algebraic functions using creative telescoping, using a computer algebra experimental mathematics learn-by-examples approach. We show that diagonals of rational functions (and this is also
Saoud Hassani +2 more
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On Hilbert modular forms, II [PDF]
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1982 Let \(A_{{\mathbb{Z}}}(\Gamma_ K)_ k\) be the \({\mathbb{Z}}\)-module of symmetric Hilbert modular forms of (integral) weight k with Fourier coefficients in \({\mathbb{Z}}\), \(A_{{\mathbb{Z}}}(\Gamma_ K):=\oplus_{r\geq 0}A_{{\mathbb{Z}}}(\Gamma_ K)_{2r}\) and \(A^ a_{{\mathbb{Z}}}(\Gamma_ K):=\oplus_{k\geq 0}A_{{\mathbb{Z}}}(\Gamma_ K)_ k\).
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From Holonomy of the Ising Model Form Factors to n-Fold Integrals and the Theory of Elliptic Curves
Symmetry, Integrability and Geometry: Methods and Applications, 2007 We recall the form factors $f^(j)_{N,N}$ corresponding to the $lambda$-extension $C(N,N; lambda)$ of the two-point diagonal correlation function of the Ising model on the square lattice and their associated linear differential equations which exhibit ...
Salah Boukraa +3 more
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From modular graph forms to iterated integrals
Journal of High Energy PhysicsModular graph forms are a class of non-holomorphic modular forms that arise in the low-energy expansion of genus-one closed string amplitudes. In this work, we introduce a systematic procedure to convert lattice-sum representations of modular graph forms
E. Claasen, M. Doroudiani
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Siegel modular forms and black hole entropy
Journal of High Energy Physics, 2017 We discuss the application of Siegel Modular Forms to Black Hole entropy counting. The role of the Igusa cusp form χ 10 in the D1D5P system is well-known, and its transformation properties are what allows precision microstate counting in this case.
Alexandre Belin +3 more
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Modular forms for three-loop banana integrals
Journal of High Energy PhysicsWe study periods of multi-parameter families of K3 surfaces, which are relevant to compute the maximal cuts of certain classes of Feynman integrals. We focus on their automorphic properties, and we show that generically the periods define orthogonal ...
Claude Duhr
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Interlacing of zeros of weakly holomorphic modular forms
Proceedings of the American Mathematical Society, Series B, 2014 We prove that the zeros of a family of extremal modular forms interlace, settling a question of Nozaki. Additionally, we show that the zeros of almost all forms in a basis for the space of weakly holomorphic modular forms of
Paul Jenkins, Kyle Pratt
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