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On Artin's Conjecture for Odd 2-dimensional Representations

  • Book
  • © 1994

Overview

Authors:
  1. Jacques Basmaji
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  2. Ian Kiming
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  3. Martin Kinzelbach
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  4. Xiangdong Wang
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  5. Loïc Merel
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Editors:
  1. Gerhard Frey
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1585)

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Table of contents (6 chapters)

  1. Front Matter

    Pages I-VIII
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  2. On the experimental verification of the artin conjecture for 2-dimensional odd galois representations over Q liftings of 2-dimensional projective galois representations over Q

    • Ian Kiming
    Pages 1-36

  3. A table of A5-fields

    • Jacques Basmaji, Ian Kiming
    Pages 37-46

  4. A. Geometrical construction of 2-dimensional galois representations of A5-type. B. On the realisation of the groups PSL2(1) as galois groups over number fields by means of l-torsion points of elliptic curves

    • Martin Kinzelbach
    Pages 47-58

  5. Universal Fourier expansions of modular forms

    • Loïc Merel
    Pages 59-94

  6. The hecke operators on the cusp forms of Γ0(N) with nebentype

    • Xiangdong Wang
    Pages 95-108

  7. Examples of 2-dimensional, odd galois representations of A5-type over ℚ satisfying the Artin conjecture

    • Ian Kiming, Xiangdong Wang
    Pages 109-121

  8. Back Matter

    Pages 122-152
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Keywords

About this book

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.

Bibliographic Information

  • Book Title: On Artin's Conjecture for Odd 2-dimensional Representations

  • Authors: Jacques Basmaji, Ian Kiming, Martin Kinzelbach, Xiangdong Wang, Loïc Merel

  • Editors: Gerhard Frey

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0074106

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1994

  • Softcover ISBN: 978-3-540-58387-5Published: 26 October 1994

  • eBook ISBN: 978-3-540-48681-7Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 156

  • Topics: Number Theory

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