Edixhoven / Couveignes 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)
Course Book
ISBN: 978-1-4008-3900-1
Verlag: De Gruyter
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, Band 176, 440 Seiten

Reihe: Annals of Mathematics Studies

No detailed description available for "Computational Aspects of Modular Forms and Galois Representations".

Autoren/Hrsg.

Edixhoven, Bas

Couveignes, Jean-Marc

Weitere Mitwirkende

de Jong, Robin

Merkl, Franz

Bosman, Johan

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Algebra Zahlentheorie

Inhaltsverzeichnis

FrontMatter, pg. i
Contents, pg. v
Preface, pg. ix
Acknowledgments, pg. x
Author information, pg. xi
Dependencies between the chapters, pg. xii
Chapter 1. Introduction, main results, context, pg. 1
Chapter 2. Modular curves, modular forms, lattices, Galois representations, pg. 29
Chapter 3. First description of the algorithms, pg. 69
Chapter 4. Short introduction to heights and Arakelov theory, pg. 79
Chapter 5. Computing complex zeros of polynomials and power series, pg. 95
Chapter 6. Computations with modular forms and Galois representations, pg. 129
Chapter 7. Polynomials for projective representations of level one forms, pg. 159
Chapter 8. Description of X1(5l), pg. 173
Chapter 9. Applying Arakelov theory, pg. 187
Chapter 10. An upper bound for Green functions on Riemann surfaces, pg. 203
Chapter 11. Bounds for Arakelov invariants of modular curves, pg. 217
Chapter 12. Approximating Vf over the complex numbers, pg. 257
Chapter 13. Computing Vf modulo p, pg. 337
Chapter 14. Computing the residual Galois representations, pg. 371
Chapter 15. Computing coefficients of modular forms, pg. 383
Epilogue, pg. 399
Bibliography, pg. 403
Index, pg. 423

Über Autor(innen)

Bas Edixhoven is professor of mathematics at the University of Leiden. Jean-Marc Couveignes is professor of mathematics at the University of Toulouse le Mirail. Robin de Jong is assistant professor at the University of Leiden. Franz Merkl is professor of applied mathematics at the University of Munich. Johan Bosman is a postdoctoral researcher at the Institut für Experimentelle Mathematik in Essen, Germany.