Errata to "Reciprocity Laws. From Euler to Eisenstein"

  • p. 444, [424]: replace Yamamoto by Yamamoto
  • p. 422, [55]: replace ``Minkowsi--Hasse'' by ``Minkowski--Hasse''
  • p. 462, [735]: replace ``Sierpinsky'' by ``Sierpinski'' [Kaplansky]
  • p. 467, [808]: replace 1895/86 by 1895/96
  • The statement of Prop. 1.5. is nonsense. What I (probably) meant is that if fx2 + gy2 = hz2 has integral solutions, then gh (hf, -fg) are quadratic residues modulo every prime divisor of f (g, h). [R. Chapman]

    Lemma 3.13: The discussion involving the index m ended up in the wrong part of the proof; see the tex/dvi/ps files for a corrected version. [R. Chapman]

    My ``proof'' of Herbrand's Theorem in Chapter 11 is nonsense. The confusion arose because I mixed two possible descriptions of the theorem: one way of looking at it is by considering Cl(K)/Cl(K)p as an FpG-module, the other is to study Clp(K) as a ZpG-module. The proof using the Stickelberger element, however, does not work over FpG because of the p in the denominator. For a corrected proof, see the ps-file of Chapter 11 that can be found here.

    Additions to "Reciprocity Laws. From Euler to Eisenstein"