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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On non-congruent numbers with 1 modulo 4 prime factors
Yi Ouyang,Shenxing Zhang +1 more
TL;DR: In this paper, the authors used the 2-decent method to find a series of odd non-congruent numbers whose prime factors are equal to or greater than the second lowest Selmer group.
Dissertation
Moduli of K3 Surfaces and Abelian Varieties
TL;DR: In this paper, a moduli space of primitively polarized K3 surfaces is constructed over Z using techniques developed by Grothendieck, Mumford, Artin and others, and the main result is that the Kuga-Satake morphism extends over an open part Spec(OEn[1/N]), where OEn is the ring of integers in En and N is a natural number explicitly depending on d, d', n and En.
Journal ArticleDOI
Connectedness of a suborbital graph for congruence subgroups
TL;DR: In this article, necessary and sufficient conditions for the graph to be connected and a forest are given. But they do not consider the problem of finding the minimum number of nodes in the graph.
Dissertation
Arithmetic Statistics for Quaternion Algebras
TL;DR: In this article, a counting law for the truncated universal family is established, with a power savings error term in the totally definite case and a geometrically meaningful constant.
Posted Content
Generalizing Benford's law using power laws: application to integer sequences
TL;DR: A simple method to derive parametric analytical extensions of Benford’s law for first digits of numerical data is proposed and it is significant that much of the analyzed integer sequences follow with a high P -value the generalized Benford distributions.