- Title Pages
- Let be defined by
- Contents
- Preface
- Acknowledgments
- Author information
- Dependencies between the chapters
-
Chapter One Introduction, main results, context -
Chapter Two Modular curves, modular forms, lattices, Galois representations -
Chapter Three First description of the algorithms -
Chapter Four Short introduction to heights and Arakelov theory -
Chapter Five Computing complex zeros of polynomials and power series -
Chapter Six Computations with modular forms and Galois representations -
Chapter Seven Polynomials for projective representations of level one forms -
Chapter Eight Description of X1(5l) -
Chapter Nine Applying Arakelov theory -
Chapter Ten An upper bound for Green functions on Riemann surfaces -
Chapter Eleven Bounds for Arakelov invariants of modular curves -
Chapter Twelve Approximating Vf over the complex numbers -
Chapter Thirteen Computing Vf modulo p -
Chapter Fourteen Computing the residual Galois representations -
Chapter Fifteen Computing coefficients of modular forms - Epilogue
- Bibliography
- Index
First description of the algorithms
First description of the algorithms
- Chapter:
- (p.69) Chapter Three First description of the algorithms
- Source:
- Computational Aspects of Modular Forms and Galois Representations
- Author(s):
Jean-Marc Couveignes
Bas Edixhoven
- Publisher:
- Princeton University Press
This chapter provides the first, informal description of the algorithms. It explains how the computation of the Galois representations V attached to modular forms over finite fields should proceed. The essential step is to approximate the minimal polynomial P of (3.1) with sufficient precision so that P itself can be obtained.
Keywords: modular forms, algorithms, Galois representation, finite fields
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- Title Pages
- Let be defined by
- Contents
- Preface
- Acknowledgments
- Author information
- Dependencies between the chapters
-
Chapter One Introduction, main results, context -
Chapter Two Modular curves, modular forms, lattices, Galois representations -
Chapter Three First description of the algorithms -
Chapter Four Short introduction to heights and Arakelov theory -
Chapter Five Computing complex zeros of polynomials and power series -
Chapter Six Computations with modular forms and Galois representations -
Chapter Seven Polynomials for projective representations of level one forms -
Chapter Eight Description of X1(5l) -
Chapter Nine Applying Arakelov theory -
Chapter Ten An upper bound for Green functions on Riemann surfaces -
Chapter Eleven Bounds for Arakelov invariants of modular curves -
Chapter Twelve Approximating Vf over the complex numbers -
Chapter Thirteen Computing Vf modulo p -
Chapter Fourteen Computing the residual Galois representations -
Chapter Fifteen Computing coefficients of modular forms - Epilogue
- Bibliography
- Index
