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Abelian surfaces over totally real fields are potentially modular
We show that abelian surfaces (and consequently curves of genus 2) over totally real fields are potentially modular. As a consequence, we obtain the...
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Ihara’s Lemma for Shimura curves over totally real fields via patching
We prove Ihara’s lemma for the mod l cohomology of Shimura curves, localized at a maximal ideal of the Hecke algebra, under a large image hypothesis...
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A Fibonacci View on the Galois NFSR Used in Trivium
Trivium is an international standard of lightweight stream ciphers (ISO/IEC 29192-3: 2012). In this paper, the Trivium-like NFSRs, a class of Galois...
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Intrinsic sub-Laplacian for hypersurface in a contact sub-Riemannian manifold
We construct and study the intrinsic sub-Laplacian, defined outside the set of characteristic points, for a smooth hypersurface embedded in a contact...
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Combinatorics and Real Lifts of Bitangents to Tropical Quartic Curves
Smooth algebraic plane quartics over algebraically closed fields of characteristic different than two have 28 bitangent lines. Their tropical...
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A Database of Hilbert Modular Forms
We describe the computation of tables of Hilbert modular forms of parallel weight 2 over totally real fields.
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Characteristic Functions and the Central Limit Theorem
The main goal of this chapter is the central limit theorem (CLT) for sums of independent random variables (Theorem 15.38) and for independent arrays...
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Skew-Adjoint Maps and Quadratic Lie Algebras
The procedure of double extension of vector spaces endowed with non-degenerate bilinear forms allows us to introduce the class of generalized
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Variational theory for the resonant T-curvature equation
In this paper, we study the resonant prescribed T -curvature problem on a compact 4-dimensional Riemannian manifold with boundary. We derive sharp...
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On Hodge-Riemann Cohomology Classes
We prove that Schur classes of nef vector bundles are limits of classes that have a property analogous to the Hodge-Riemann bilinear relations. We...
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Simplicial Sets in Topology, Category Theory, and Beyond
The notion of a simplicial set originated in algebraic topology and has also been utilized extensively in category theory, but until relatively...
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Stability of Rotation Relations of Three Unitaries with the Flip Action in C*-Algebras
The authors show that if Θ = ( θ jk ) is a 3 × 3 totally irrational real skew-symmetric matrix, where θ jk ∈ [0, 1) for j, k = 1, 2, 3, then for any ε >...
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A Study of Energy Band Rearrangement in Isolated Molecules by Means of the Dirac Oscillator Approximation
Energy band rearrangement along a control parameter in isolated molecules is studied through axially symmetric Hamiltonians describing the coupling...
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Incoherent Definite Spaces and Shimura Varieties
In this paper, we define incoherent definite quadratic spaces over totally real number fields and incoherent definite Hermitian spaces over CM...
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On the rank of general linear series on stable curves
We study the dimension of loci of special line bundles on stable curves and for a fixed semistable multidegree. In case of total degree
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Controlling the BMO Semi-Norm of the Unit Normal
Earlier we have estimated a certain brand of singular integral operators in terms of the geometry of the underlying “surface” in terms of the BMO...