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A Course in Arithmetic
TLDR
In this article, the theorem on arithmetic progressions modular forms is proved for finite fields p-adic fields Hilbert symbol quadratic forms over Qp, and over Q integral quadratics forms with discriminant +-1.Abstract:
Part 1 Algebraic methods: finite fields p-adic fields Hilbert symbol quadratic forms over Qp, and over Q integral quadratic forms with discriminant +-1. Part 2 Analytic methods: the theorem on arithmetic progressions modular forms.read more
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Symmetric products, permutation orbifolds and discrete torsion
TL;DR: In this paper, permutation permutation orbifolds of the full symmetric group S n are considered by applying the general techniques of permutation Orbifolds, i.e. generating functions for various quantities, e.g. the torus partition functions and the Klein-bottle amplitudes.
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Frobenius manifold structure on orbit space of Jacobi groups; Part II
TL;DR: In this paper, the authors identify the generators of the algebra of Jacobi forms with the moduli of Hurwitz spaces of meromorphic functions over elliptic curves and construct a Frobenius structure on it, computing the free energy and the flat coordinates of the corresponding solution to WDVV equations of associativity.
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The automorphism group of the derived category for a weighted projective line
Helmut Lenzing,Hagen Meltzer +1 more
TL;DR: In this article, it was shown that up to a translation each automorphism of the derived category D b X of coherent sheaves on a weighted projective line X, equiv-alently of D b A of finite dimensional modules over a derived canonical algebra A, is composed of tubular mutations and automorphisms of X.
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Strict ergodicity of affine p-adic dynamical systems on Zp
TL;DR: In this paper, it was shown that the dynamical system (Z p, T α, β ) is minimal if and only if α ∈ 1 + p r p Z p and β is a unit, and when it is not minimal, it is strictly ergodic and topologically conjugate with an analytic and isometric conjugacy.
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K3 Surfaces and String Duality
TL;DR: The main purpose of these lecture notes is to explore the moduli space of type IIA, type IIB, and heterotic string compactified on a K3 surface as discussed by the authors.