scispace - formally typeset
Open AccessBook

A Course in Arithmetic

Jean-Pierre Serre
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
Posted Content

Moduli of Riemann Surfaces, Transcendental Aspects

Richard Hain
- 24 Mar 2000 - 
TL;DR: In this paper, an informal set of lecture notes on moduli spaces of curves based on a set of lectures given at the ICTP last summer is presented. The point of view is generally topological and analytical.
Posted Content

The orbit method and analysis of automorphic forms

Paul D. Nelson, +1 more
- 20 May 2018 - 
TL;DR: In this paper, the authors developed the orbit method in a quantitative form, along the lines of microlocal analysis, and applied it to the analytic theory of automorphic forms.
Book ChapterDOI

Signatures Through Approximate Representations by Quadratic Forms

H. Ong, +1 more
TL;DR: A signature scheme where the private key is a random (n, n)-matrix T with coefficients in ℤm/mℤ, m a product of two large primes, which is faster than the RSA-scheme and knowledge of this prime decomposition enables forging signatures.
Journal ArticleDOI

Frobenius–Schur indicators in Tambara–Yamagami categories

Kenichi Shimizu
- 15 Apr 2011 - 
TL;DR: In this paper, the Fourier transform on finite abelian groups is used to define Frobenius-Schur indicators of simple objects of Tambara-Yamagami categories.
Posted Content

Vertex Operators and Modular Forms

Geoffrey Mason, +1 more
- 24 Sep 2009 - 
TL;DR: In this paper, the idea of vertex operator algebra (VOA) and the relationship between VOAs and elliptic functions and modular forms is discussed. But the main point of these notes is to explain how this works, and to give some reasonably interesting examples.