Open AccessBook
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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Journal ArticleDOI
Detecting perfect powers in essentially linear time
TL;DR: An algorithm to compute approximate kth roots and it is proved, using Loxton's theorem on multiple linear forms in logarithms, that this perfect-power decomposition algorithm runs in time (log n) 1+o(1) .
Book ChapterDOI
Arithmetic invariant theory
TL;DR: In this article, the problem of arithmetic invariant theory when k is not algebraically closed has been studied in the context of regular semisimple orbits, i.e., the closed orbits whose stabilizers have minimal dimension in three arithmetically rich representations of the split odd special orthogonal group.
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IIB flux non-commutativity and the global structure of field theories
TL;DR: In this paper, the authors discuss the origin of the choice of global structure for six-dimensional (2,0) theories and their compactifications in terms of their realization from IIB string theory on ALE spaces.
Journal ArticleDOI
Squares of Random Linear Codes
TL;DR: In this article, the authors give a positive answer for linear codes of dimension $k$ and length roughly 1/2k^2$ or smaller, and show that convergence speed is exponential if the difference $k(k+1)/2-n$ is at least linear in $k$.