Computational Aspects of Modular Forms and Galois Representations : : How One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime (AM-176) /

Computational Aspects of Modular Forms and Galois Representations : : How One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime (AM-176) / / ed. by Bas Edixhoven, Jean-Marc Couveignes.

Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices. Their Fourier coefficients, with Ramanujan's tau-function as a typical example, have deep arithmetic significance. Prior to this book, the fastest k...

Full description

Saved in:
Bibliographic Details
Superior document:Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
MitwirkendeR:
Bosman, Johan,
Couveignes, Jean-Marc,
Edixhoven, B.,
Edixhoven, Bas,
Merkl, Franz,
de Jong, R.,
de Jong, Robin,
TeilnehmendeR:
Bosman, Johan.
Merkl, Franz.
de Jong, Robin.
HerausgeberIn:
Couveignes, Jean-Marc,
Edixhoven, Bas,
Place / Publishing House:Princeton, NJ : : Princeton University Press, , [2011]
©2011
Year of Publication:2011
Edition:Course Book
Language:English
Series:Annals of Mathematics Studies ; 176
Online Access:
Physical Description:1 online resource (440 p.) :; 6 line illus.
Tags: Add Tag
No Tags, Be the first to tag this record!
Table of Contents:
  • Frontmatter
  • Contents
  • Preface
  • Acknowledgments
  • Author information
  • Dependencies between the chapters
  • Chapter 1. Introduction, main results, context
  • Chapter 2. Modular curves, modular forms, lattices, Galois representations
  • Chapter 3. First description of the algorithms
  • Chapter 4. Short introduction to heights and Arakelov theory
  • Chapter 5. Computing complex zeros of polynomials and power series
  • Chapter 6. Computations with modular forms and Galois representations
  • Chapter 7. Polynomials for projective representations of level one forms
  • Chapter 8. Description of X1(5l)
  • Chapter 9. Applying Arakelov theory
  • Chapter 10. An upper bound for Green functions on Riemann surfaces
  • Chapter 11. Bounds for Arakelov invariants of modular curves
  • Chapter 12. Approximating Vf over the complex numbers
  • Chapter 13. Computing Vf modulo p
  • Chapter 14. Computing the residual Galois representations
  • Chapter 15. Computing coefficients of modular forms
  • Epilogue
  • Bibliography
  • Index

Similar Items