Reciprocity Laws II. From Kummer to Hilbert
Quadratic reciprocity laws in quadratic number fields
13. Eisenstein's Conjecture
Eisenstein's 'derivation' of the l-th power reciprocity law
in cyclotomic fields
14. Analytic Techniques
15. Genus Theory
16. Kummer's Reciprocity Law
17. Hilbert's Reciprocity Law
18. Hecke's Gauss Sums and Quadratic Reciprocity
19. Theta Functions
20. Norm Residues
21. Hilbert Class Field Theory
22. Quaternion Algebras
23. Quadratic Function Fields
I hope to have preliminary versions of these chapters up here
until the end of 2005. Comments are more than welcome. Please
let me know about mistakes, typos, omissions, ...