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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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Book ChapterDOI
Diophantine geometry and non-abelian reciprocity laws I
Minhyong Kim,Minhyong Kim +1 more
TL;DR: In this paper, the authors use non-abelian fundamental groups to define a sequence of higher reciprocity maps on the adelic points of a variety over a number of fields satisfying certain conditions in Galois cohomology.
Book
A Gentle Course in Local Class Field Theory: Local Number Fields, Brauer Groups, Galois Cohomology
TL;DR: In this paper, a self-contained exposition of local class field theory is presented, serving as a second course on Galois theory, with a discussion of several fundamental topics in algebra, such as profinite groups, padic fields, semisimple algebras and their modules, and homological algebra with the example of group cohomology.
Journal ArticleDOI
Renormalization group properties of the conformal mode of a torus
Matthew P. Kellett,Tim R. Morris +1 more
TL;DR: In this paper, it was shown that the Wilsonian renormalization group properties of the conformal factor of the metric are profoundly altered by the fact that it has a wrong-sign kinetic term.
Journal ArticleDOI
The 8-rank of tame kernels of quadratic number fields
Xuejun Guo,Hourong Qin +1 more
TL;DR: Theorem 1.1. For any finite abelian group H of exponent 8 with rk2(H) ≥ 2 + rk4(H), there are infinitely many real quadratic fields F such that K2OF /(K2OF )'H as mentioned in this paper.