On Artin's Conjecture for Odd 2-dimensional Representations

  • Authors
  • Jacques Basmaji
  • Ian Kiming
  • Martin Kinzelbach
  • Xiangdong Wang
  • Loïc Merel
  • Editors
  • Gerhard Frey

Part of the Lecture Notes in Mathematics book series (LNM, volume 1585)

About this book

Introduction

The main topic of the volume is to develop efficient algorithms by which one can verify Artin's conjecture for odd two-dimensional representations in a fairly wide range. To do this, one has to determine the number of all representations with given Artin conductor and determinant and to compute the dimension of a corresponding space of cusp forms of weight 1 which is done by exploiting the explicit knowledge of the operation of Hecke operators on modular symbols.
It is hoped that the algorithms developed in the volume can be of use for many other problems related to modular forms.

Keywords

Artin's conjecture for L-series Cusp forms Galois group Modular symbols Volume algorithms construction elliptic curve form knowledge modular form presentation torsion verification

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0074106
  • Copyright Information Springer-Verlag Berlin Heidelberg 1994
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-58387-5
  • Online ISBN 978-3-540-48681-7
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book