Genus Two Hyperelliptic Drinfeld Modules over F2

Chapters in this book

1. Frontmatter I
2. Preface V
3. A Brief Introduction to Drinfeld Modules 1
4. Galois Calculus and Carlitz Exponentials 33
5. A Two-Dimensional Analogue of Stickelberger's Theorem 51
6. On Gamma Functions for Function Fields 75
7. Groups of Elliptic Units in Global Function Fields 87
8. Class Number “Parity” for Cyclic Function Fields 103
9. Genus Two Hyperelliptic Drinfeld Modules over F2 117
10. A Short Introduction to Rigid Analytic Spaces 131
11. Lecture on Rigid Geometry 143
12. Moduli for Drinfeld Modules 153
13. Ramifications Arising from Drinfeld Modules 171
14. Rigid Analytic Modular Forms: An Integral Transform Approach 189
15. Some Results on the Jacobians of Drinfeld Modular Curves 209
16. Some Integrals Attached to Modular Forms in the Theory of Function Fields 227
17. Transcendence in Finite Characteristic 253
18. Indépendance Algébrique des Périodes et Quasi-périodes d'un Module de Drinfeld 265
19. Géométrie Diophantienne sur les Modules de Drinfeld 285
20. Transcendence Properties of Carlitz Zeta-values 303
21. L-series of t-motives and Drinfeld Modules 313
22. Classgroups of Sheaves of Locally Free Modules over Global Function Fields 403
23. Artin-Schreier-Witt Extensions as Limits of Kummer-Lubin-Tate Extensions, and the Explicit Reciprocity Law 413
24. The Circle Method and the Strict Waring Problem in Function Fields 421
25. Ramsey's Theorem and Waring's Problem for Algebras over Fields 435
26. Sums of Three Cubes 443
27. Heights and Zeta Functions in Function Fields 455
28. Continued Fraction Characterization and Generic Ideals in Real Quadratic Function Fields 465
29. Dictionary 475
30. Backmatter 483