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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Introduction to Elliptic Fibrations
TL;DR: The modern study of elliptic fibrations started in the early 1960s with seminal works by Kodaira and by Neron as discussed by the authors, and they play a central role in the classification of algebraic surfaces, in many aspects of arithmetic geometry, theoretical physics and string geometry.
Journal ArticleDOI
Relations in a quantized elastica
TL;DR: In this article, Matsutani et al. showed the hyperelliptic solutions of a loop soliton as a study of a quantized elastica, and studied relations between the quantised elastica and integrals of its Schwarz derivative.
Book ChapterDOI
A q-product Tutorial for a q-series Maple Package
TL;DR: The q-series Maple package as discussed by the authors provides facilities for conversion between q-Series and q-products and finding algebraic relations between Q-series and Q-product factorisations, as well as other applications involving factorisations into theta functions and etaproducts.
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Box-counting fractal strings, zeta functions, and equivalent forms of Minkowski dimension
TL;DR: In this paper, a number of techniques for determining the Minkowski dimension of bounded subsets of some Euclidean space of any dimension, including: the box-counting dimension and equivalent definitions based on various boxcounting functions; the similarity dimension via the Moran equation (at least in the case of self-similar sets); the order of the (box-)counting function; the classic result on compact subsets on the real line due to Besicovitch and Taylor, as adapted to the theory of fractal strings; and the abscissae of
Journal ArticleDOI
Almost-universal quadratic forms: An effective solution of a problem of Ramanujan
J. Bochnak,Byeong-Kweon Oh +1 more
TL;DR: In this article, the authors investigated almost universal positive-definite integral quaternary quadratic forms, that is, those representing sufficiently large positive integers, and provided an effective characterization of all such forms.