Re- and Preprints:

Class Groups

title journal file
Kuroda's Class Number Formula Acta Arith. 66 (1994), 245-260 pdf
Class groups of cyclotomic number fields I Acta Arith. 72 (1995), 347-359 pdf
Class groups of cyclotomic number fields II Acta Arith. 84 (1998), 59-70 pdf
On the 4-rank of class groups of real quadratic number fields unpublished pdf
On class number 1 problems of some normal CM fields of degree 24 J. Theor. Nombres Bordx. 11 (1999), 387-406 pdf
Galois Action on Class Groups J. Algebra 264 (2003), 553-564 pdf
Class Groups of Dihedral Extensions Math. Nachr 278 (2005), 679-691 pdf

Reciprocity Laws

Rational Quartic Reciprocity Acta Arith. 67 (1994), 387--390 pdf
Rational Quartic Reciprocity II Acta Arith. 80 (1997), 273--276 pdf
Reciprocity Laws. From Euler to Eisenstein Springer Verlag html
Reciprocity Laws. From Kummer to Hilbert Springer Verlag; in preparation html
Bibliography on Reciprocity Laws www html
A list of proofs of the Quadratic Reciprocity Law. www html

Euclidean Number Fields

The Euclidean Algorithm in Algebraic Number Fields; Expo. Math. 13 (1995), 385-416. pdf
The Euclidean Algorithm in cubic number fields (with Stefania Cavallar) Proceedings Number Theory Eger 1996, (Györy, Pethö, Sos eds.), Gruyter 1998, 123-146 pdf
On Gauss Bounds of quadratic extensions of imaginary quadratic Euclidean number fields Publ. Math. Debrecen 50 (1997), 365-368 pdf
Euclidean Windows (with Stefania Cavallar) LMS J. Comput. Math. 3 (2000), 335-355 pdf
Quartic Euclidean Number Fields unpublished pdf
Online Bibliography on Euclidean Rings www html

Class Field Theory

On 2-class field towers of imaginary quadratic number fields; J. Theor. Nombres Bordeaux 6 (1994), 261-272 pdf
Construction of Hilbert 2-Class Fields Short introduction to my thesis pdf
On unramified quaternion extensions of quadratic number fields J. Theor. Nombres Bordeaux 9 (1997), 51-68 pdf
Imaginary quadratic number fields with cyclic Cl2(k1) (with E. Benjamin and C. Snyder J. Number Theory 67 (1997), 229-245 pdf
Real quadratic number fields with Abelian Gal(k2/k) (with Elliot Benjamin and Chip Snyder) J. Number Theory 73 (1998), 182-194 pdf
On the 2-class field tower of some imaginary quadratic number fields Abh. Math. Sem. Hamburg 67 (1997), 205-214 pdf
Imaginary quadratic fields k with Cl2(k) = (2,2m) and d(Cl2(k1)) = 2 (with Elliot Benjamin and Chip Snyder) Pac. J. Math. 198 (2001), 15-31 pdf
Imaginary quadratic fields with Cl2(k) = (2,2,2) (with E. Benjamin and C. Snyder) J. Number Theory pdf
A survey on Class Field Towers www html
Postscript to the English translation of Koch's Galois theory of p-extensions (with H. Koch) Springer-Verlag, August 2002 pdf
Selmer groups and quadratic reciprocity preprint separants-0 pdf
Kronecker-Weber via Stickelberger J. Théor. Nombres Bordeaux 17 (2005), 579--582 pdf

Elliptic Curves

On Tate-Shafarevich groups of some elliptic curves; Algebraic number theory and Diophantine analysis (Graz, 1998), 277-291; de Gruyter, 2000 pdf
A note on Pépin's counter examples to the Hasse principle for curves of genus 1 Abh. Math. Sem. Hamburg 69 (1999), 335-345 pdf
Some families of noncongruent numbers Acta Arithmetica 110 (2003), 15-36 pdf
On Tate-Shafarevich groups of y2 = x(x2 - k2) (with R. Mollin) Acta Math. Univ. Comenianae 72 (2003), 73-80 pdf


Introduction (with Norbert Schappacher) to the English translation of Hilbert's Zahlbericht by I. Adamson Springer-Verlag pdf
Development of the principal genus theorem (from Gauss to Noether) Springer-Verlag 2003, proceedings of a conference on 200 years of Disquisitiones Arithmeticae in Oberwolfach 2001 pdf
HIstory of Number Theory Collection of online material on the history of number theory, including webliographies and letters between Hasse, R. Brauer and E. Noether. html


Kreise und Quadrate modulo p Mathem. Semesterberichte 47 (2000), 51-73 pdf
Conics: a Poor Man's Elliptic Curves preprint pdf
Higher Descent on Pell Conics I. From Legendre to Selmer preprint pdf
Higher Descent on Pell Conics II. Two Centuries of Missed Opportunities draft pdf
Higher Descent on Pell Conics III. The First $2$-Descent draft pdf
Simple counterexamples to the Local-Global principle (with W. Aitken) draft pdf
Euler's Trick and second 2-descents (with Ö. Öztürün) draft pdf
The Pell Equation webliography up to 1945 html

The Rest

Small norms in a quadratic field; an introductory section to the paper on simplest cubic fields that was omitted in the published version unpublished pdf
On Simplest Cubic Fields (with A. Pethö); Manuscripta Math. 88 (1995), 53--58 pdf
The Snake Lemma (new version Nov. 2002) unpublished pdf
Unsolved problems in Algebraic Number Theory unpublished pdf

Translations of some articles

Boas Erez: an introduction to the fascinating topic of normal integral bases (in German; hey, the original is Italian!) Representations of groups in algebraic number theory. An introduction. (Italian) Mathematics, Proc. Colloq., Locarno/Italy 1988-1989, Note Mat. Fis. 3, vol. 4, 41-65 (1990). pdf
Coates & and Poitou: An account of the history of the main conjecture as proved by Mazur and Wiles Du nouveau sur les racines de l'unité (French) Gaz. Math., Soc. Math. Fr. 15, 5-26 (1980). pdf
Serre: On congruences involving Ramanujan's tau-function and their interpretation in terms of l-adic representations Une interpretation des congruences relatives a la fonction de Ramanujan (French) Semin. Delange-Pisot-Poitou 9 (1967/68), Theorie Nombres, No.14, 17p. (1969) pdf
Velu: Exposition of Serre's article on the Galois properties of division points on elliptic curves Groupes de Galois attachés aux points d'ordre fini des courbes elliptiques sur un corps de nombres (d'après J. P. Serre). (French) Sem. Theorie Nombres 1971-1972, Univ. Bordeaux, No.30, 12 p. (1972) pdf
M. Waldschmidt: An introduction to complex multiplication of elliptic curves. notes rédigées par A. Faisant, R. Lardon et G. Philibert, Sém Arithm. Univ. St Etienne, 1981-82, No 4, 23 pp. pdf
Guy Henniart: The congruent number problem and its connections with elliptic curves and modular forms. some journal of the SMF ? pdf
Koch: Über den 2-Klassenkörperturm eines quadratischen Zahlkörpers J. Reine Angew. Math. 214/215 (1964), 201--206. pdf
Hasse: Vorlesungen über Klassenkörpertheorie. Teil I. Galois Theory Physica Verlag Würzburg pdf
 Last update: September 10, 2003