- 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
Modular curves, modular forms, lattices, Galois representations
Modular curves, modular forms, lattices, Galois representations
- Chapter:
- (p.29) Chapter Two Modular curves, modular forms, lattices, Galois representations
- Source:
- Computational Aspects of Modular Forms and Galois Representations
- Author(s):
Bas Edixhoven
- Publisher:
- Princeton University Press
This chapter provides the necessary background concerning modular curves and modular forms. It covers modular curves, modular forms, lattices and modular forms, Galois representations attached to eigenforms, and Galois representations over finite fields and reduction to torsion in Jacobians.
Keywords: modular forms, modular curves, lattices, Galois representations, eigenforms, finite fields, torsion, Jacobians
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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
