Re- and Preprints:
Here's A list of publications.
For reprints and updates in pdf format, go to my
- The MR-abstract of my paper on Kuroda's
Class Number Formula; Acta Arith. 66 (1994), 245--260
- On class groups
of cyclotomic number fields I; Acta Arith. 72 (1995), 347--359;
- On class groups
of cyclotomic number fields II; Acta Arith. 84 (1998), 59--70
- On class groups of cyclotomic number fields III; (coming soon)
- On the 4-rank of class groups of
real quadratic number fields, with a new proof of C. Maire's
result that the 2-class field tower of such fields is
infinite if their 4-rank is at least 4.
- The solution of the class number 1 problem
for CM fields of degree 24 whose Galois group has the alternating
group A4 as a quotient (with Stephane Louboutin and Ryotaro Okazaki).
Final version. J. Theor. Nombres 11 (1999), 387-406
- On Rational Quartic Reciprocity;
Acta Arith. 67 (1994), 387--390; MR
- Rational Quartic Reciprocity II ;
Acta Arith. 80 (1997), 273--276; generalizes the first part to
composite values of the denominator.
- Here is a link to my book on the
Reciprocity Laws from Euler to Eisenstein. Part II
on the development from Kummer to Artin is currently being
- An online Bibliography on Reciprocity Laws;
- A list of Proofs of the Quadratic
Euclidean Number Fields
- A survey on Euclidean Number Fields;
also available as a gzipped dvi file.
This is an update of the article in Expo. Math. 13 (1995), 385-416.
Last update: Oct. 29, 1999.
- On The Euclidean Algorithm in Cubic Fields
(with Stefania Cavallar); Proc. Number Theory Eger 1996 (1998), 123--146;
- On Gauss Bounds of quadratic extensions
of imaginary quadratic Euclidean number fields; Publ. Math. Debrecen
50 (1997), 365--368
- Euclidean Windows (with Stefania Cavallar);
LMS J. Comput. Math.
3 (2000), 335-355
- A manuscript on the classification of the norm-Euclidean bicyclic
complex quartic fields (ps)
- An online Bibliography on Euclidean Rings.
Class Field Towers
- The MR review of my paper on
2-class field towers of imaginary quadratic number fields;
J. Theor. Nombres Bordeaux 6 (1994), 261--272
- On the Construction of Hilbert 2-Class Fields
is a very short introduction to my thesis;
- On unramified quaternion extensions of
quadratic number fields; J. Theor. Nombres Bordeaux 9 (1997), 51--68
- The determination of all real quadratic
number fields whose $2$-class field tower is abelian
(with E. Benjamin and C. Snyder); J. Number Theory 73 (1998), 182--194
- The determination of all imaginary quadratic
number fields whose 2-class field has a cyclic 2-class group
(with E. Benjamin and C. Snyder); J. Number Theory 67 (1997), 229--245
- On the determination of the 2-class field tower
of a certain family of imaginary quadratic number fields;
Abh. Math. Sem. Hamburg 67 (1997), 205--214
- Imaginary quadratic fields k with
Cl_2(k) = (2,2^m) and d(Cl_2(k^1)) = 2 (May 1999, with
E. Benjamin and C. Snyder; Pac. J. Math, to appear)
- A search for imaginary quadratic number fields with 2-class field
tower of length 3 (with E. Benjamin and C. Snyder, in preparation)
- A survey on Class Field Towers
- They have their own page.
- On Tate-Shafarevich groups of some elliptic curves;
Algebraic number theory and Diophantine analysis (Graz, 1998), 277--291
- A note on Pepin's counter examples to the Hasse
Principle for curves of genus 1; Abh. Math. Sem. Hamburg 69 (1999),
335-345. Meanwhile I discovered a beautiful article by
Noam Elkies that also mentions the approach to FLT for N = 7
using 2-descent on elliptic curves: be sure to check out
"The Klein Quartic in Number Theory" in "The Eightfold Way",
S. Levy (Ed.), MSRI Publications 35 (1999), Cambridge Univ. Press.
- On the capitulation of Tate-Shafarevich groups (coming soon)
- Some families of non-congruent numbers (coming soon)
- On Simplest Cubic Fields (with A. Pethoe);
Manuscripta Math. 88 (1995), 53--58; MR
- The Introduction (with Norbert Schappacher)
to the English translation of Hilbert's Zahlbericht by I. Adamson
that has just been published by Springer Verlag.
- A note on the Snake Lemma
- On Circles, Primes and Quadratic Residues
(draft, June 1999). The final version is in German and called
Kreise und Quadrate modulo p,
Mathem. Semesterberichte 47 (2000), 51-73
- I'm starting to compile a list of Unsolved
Problems in algebraic number theory.
- Von einer Einfuehrung in die Kohomologie von Gruppen fuer
Zahlentheoretiker ist Kapitel I
jetzt fertig. An Vorkenntnissen werden algebraische
Zahlentheorie (Ideale, p-adische Koerper, Galoistheorie)
- Here are some translations of
Last update: Oct 27, 1999