On Artins Conjecture For Odd 2 Dimensional Representations

Download or read book On Artin's Conjecture for Odd 2-dimensional Representations written by Gerhard Frey and published by Springer. This book was released on 2006-11-15 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.