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A Course in Arithmetic
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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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The Dimension of Spaces of Vector-Valued Modular Forms of Integer Weight
TL;DR: In this paper, a dimension formula for spaces of vector-valued modular forms of integer weight in case the associated multiplier system has finite image is presented, and the weight distribution of the module generators of holomorphic and cusp forms, as well as the duality relation between cusp and holomorphic forms for the contragredient are discussed.
Journal ArticleDOI
On the compactification of the bosonic string at higher loops
TL;DR: In this paper, the authors analyze the procedure of string compactification on a lattice Λ in the framework of Polyakov's path integral for arbitrary genus of the string world sheet and demonstrate how compactification, factorizability into left and right movers and modular invariance are related.
Dissertation
Autour des déformations de Rankin-Cohen.
TL;DR: In this paper, a nouvelle interpretation des deformations de Rankin-Cohen via la theorie de "Quantification par Deformations de Fedosov" was presented.
Dissertation
Some Generalizations and Properties of Balancing Numbers
TL;DR: In this paper, the authors define gap balancing numbers, which allow generalization in two different ways: the first way is through altering coefficients occurring in its binary recurrence sequence and the second way involves modification of its defining equation, thereby allowing more than one gap.
Journal ArticleDOI
Some Identities and Asymptotics for Characters of the Symmetric Group
A Klyachko,E Kurtaran +1 more
TL;DR: In this paper, the problem of counting triangulations was reduced to counting ramified coverings p : X a Y of a Riemann surface Y of genus g and irreducible characters x of the Y symmetric group S, n s deg p.