Open AccessBook
A Course in Arithmetic
Reads0
Chats0
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
Citations
More filters
Journal ArticleDOI
Generalized arithmetic intersection numbers
TL;DR: In this article, the authors present an arithmetic intersection theory for hermitian line bundles on arithmetic surfaces, where the metrics are allowed to have logarithmic singularities at a finite set of points.
Journal ArticleDOI
The distribution of closed geodesics on the modular surface, and Duke's theorem
TL;DR: In this paper, an ergodic theoretic proof of a theorem of Duke about equidistribution of closed geodesics on the modular surface is given, which is closely related to the work of Yu and Skubenko.
Posted Content
Logarithmic growth of systole of arithmetic Riemann surfaces along congruence subgroups
TL;DR: In this paper, the authors apply a study of orders in quaternion algebras, to the differential geometry of Riemann surfaces, and obtain a new trace estimate valid for an arbitrary ideal in a quaternian algebra.
Journal ArticleDOI
Reflection groups in algebraic geometry
TL;DR: A survey of appearances of these groups in various areas of algebraic geometry can be found in this article, with a brief exposition of the theory of discrete reflection groups in spherical, euclidean and hyperbolic geometry as well as their analogs in complex spaces.