Results 61 to 70 of about 378,592 (232)
Modular A 5 symmetry for flavour model building
Journal of High Energy Physics, 2019 In the framework of the modular symmetry approach to lepton flavour, we consider a class of theories where matter superfields transform in representations of the finite modular group Γ5 ≃ A 5.
P. P. Novichkov +3 more
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Families of modular forms [PDF]
Journal de Théorie des Nombres de Bordeaux, 2001 The author gives a down-to-earth introduction to the theory of \(p\)-adic families of modular forms, and presents an elementary proof of \textit{D. Wan}'s result [Invent. Math. 133, No.~2, 449--463 (1998; Zbl 0907.11016)] that the Newton polygon of the \(U_p\)-operator acting on \(S_k(\Gamma_1(N_p))\) is bounded below by an explicit quadratic lower ...
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Non-holomorphic modular forms from zeta generators
Journal of High Energy PhysicsWe study non-holomorphic modular forms built from iterated integrals of holomorphic modular forms for SL(2, ℤ) known as equivariant iterated Eisenstein integrals.
Daniele Dorigoni +7 more
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All-order differential equations for one-loop closed-string integrals and modular graph forms
Journal of High Energy Physics, 2020 We investigate generating functions for the integrals over world-sheet tori appearing in closed-string one-loop amplitudes of bosonic, heterotic and type-II theories.
Jan E. Gerken +2 more
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Counting curves with modular forms [PDF]
Nuclear Physics B, 1996 Minor changes, added references, 12 pages, uses ...
Gregory W. Moore, Måns Henningson
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MOCK THETA FUNCTIONS AND QUANTUM MODULAR FORMS
Forum of Mathematics, Pi, 2013 Ramanujan’s last letter to Hardy concerns the asymptotic properties of modular forms and his ‘mock theta functions’. For the mock theta function $f(q)$, Ramanujan claims that as $q$ approaches an even-order $2k$ root of unity, we have $$\begin{eqnarray ...
AMANDA FOLSOM +2 more
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Inventiones Mathematicae, 1990 \textit{P. Deligne} defined in Sémin. Bourbaki 1968/69, Exp. No. 355, Lect. Notes Math. 179, 139--172 (1971; Zbl 0206.49901) the \(\ell\)-adic parabolic cohomology groups attached to holomorphic cusp forms of weight \(\geq 2\) on congruence subgroups of \(\mathrm{SL}_2(\mathbb{Z})\) as certain subgroups in the \(\ell\)-adic cohomology of Kuga-Sato ...
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On Viazovska’s modular form inequalities
Proceedings of the National Academy of Sciences, 2023 Viazovska proved that the E 8 lattice sphere packing is the densest sphere packing in 8 dimensions. Her proof relies on
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Moduli for Pairs of Elliptic Curves with Isomorphic N-torsion [PDF]
, 1998 We study the moduli surface for pairs of elliptic curves together with an isomorphism between their N-torsion groups. The Weil pairing gives a "determinant" map from this moduli surface to (Z/NZ)*; its fibers are the components of the surface.
Carlton, David
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On Teichm�ller modular forms [PDF]
Mathematische Annalen, 1994 The author studies global sections of the automorphic line bundles on the moduli space of algebraic curves. In particular, he constructs an analogue of Fourier expansion for these sections over fields of characteristic \(\neq 2\), based on nonarchimedean Schottky uniformization theory.
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