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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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p-Adic valuation of weights in Abelian codes over /spl Zopf/(p/sup d/)
TL;DR: The analogs of McEliece's theorem obtained by Wilson (for Hamming weight, Lee weight, and symbol counts) and the analog obtained here for Euclidean weight are sharp in the sense that they give the maximum power of 2 that divides the weights of all the codewords whose Fourier transforms have a specified support.
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Classification of extremal elliptic K3 surfaces and fundamental groups of open K3 surfaces
Ichiro Shimada,De-Qi Zhang +1 more
TL;DR: A complete list of extremal elliptic K3 surfaces can be found in this article, with a sufficient condition for topological fundamental group of complement to an ADE-configuration of smooth rational curves on a K3 surface to be trivial.
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Quadratic Forms over Z from Diophantus to the 290 Theorem
TL;DR: A brief historical survey of the representation theory of quadratic forms over the integers can be found in this paper, which is self-contained in the sense that all the basic definitions and concepts are provided.
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CFTs on Riemann surfaces of genus g ≥ 1
TL;DR: In this article, the authors established explicit formulas for the 2-point function of the Virasoro field on hyperelliptic Riemann surfaces of genus $g\geq 1.