## Class Groups |
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title | journal | file |

Kuroda's Class Number Formula | Acta Arith. 66 (1994), 245-260
| |

Class groups of cyclotomic number fields I | Acta Arith. 72 (1995), 347-359
| |

Class groups of cyclotomic number fields II | Acta Arith. 84 (1998), 59-70
| |

On the 4-rank of class groups of real quadratic number fields | unpublished | |

On class number 1 problems of some normal CM fields of degree 24 | J. Theor. Nombres Bordx. 11 (1999), 387-406
| |

Galois Action on Class Groups | J. Algebra 264 (2003), 553-564
| |

Class Groups of Dihedral Extensions | Math. Nachr 278 (2005), 679-691
| |

## Reciprocity Laws |
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Rational Quartic Reciprocity | Acta Arith. 67 (1994), 387--390
| |

Rational Quartic Reciprocity II | Acta Arith. 80 (1997), 273--276
| |

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 |
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The Euclidean Algorithm in Algebraic Number Fields; | Expo. Math. 13 (1995), 385-416.
| |

The Euclidean Algorithm in cubic number fields (with Stefania Cavallar) | Proceedings Number Theory Eger 1996, (Györy, Pethö, Sos eds.), Gruyter 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
| |

Quartic Euclidean Number Fields | unpublished | |

Online Bibliography on Euclidean Rings | www | html |

## Class Field Theory |
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On 2-class field towers of imaginary quadratic number fields; | J. Theor. Nombres Bordeaux 6 (1994), 261-272
| |

Construction of Hilbert 2-Class Fields | Short introduction to my thesis | |

On unramified quaternion extensions of quadratic number fields | J. Theor. Nombres Bordeaux 9 (1997), 51-68
| |

Imaginary quadratic number fields with cyclic
Cl_{2}(k^{1})
(with E. Benjamin and C. Snyder
| J. Number Theory 67 (1997), 229-245
| |

Real quadratic number fields with Abelian Gal(k^{2}/k)
(with Elliot Benjamin and Chip Snyder)
| J. Number Theory 73 (1998), 182-194
| |

On the 2-class field tower of some 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
(with Elliot Benjamin and Chip Snyder)
| Pac. J. Math. 198 (2001), 15-31
| |

Imaginary quadratic fields with Cl_{2}(k) = (2,2,2)
(with E. Benjamin and C. Snyder)
| J. Number Theory | |

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 | |

Selmer groups and quadratic reciprocity | preprint separants-0 | |

Kronecker-Weber via Stickelberger | J. Théor. Nombres Bordeaux 17 (2005), 579--582
| |

## Elliptic Curves |
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On Tate-Shafarevich groups of some elliptic curves; | Algebraic number theory and Diophantine analysis (Graz, 1998), 277-291; de Gruyter, 2000 | |

A note on Pépin's counter examples to the Hasse principle for curves of genus 1 | Abh. Math. Sem. Hamburg 69 (1999), 335-345
| |

Some families of noncongruent numbers | Acta Arithmetica 110 (2003), 15-36
| |

On Tate-Shafarevich groups of
y^{2} = x(x^{2} - k^{2})
(with R. Mollin)
| Acta Math. Univ. Comenianae 72 (2003), 73-80
| |

## Historical |
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Introduction (with Norbert Schappacher) to the English translation of Hilbert's Zahlbericht by I. Adamson | Springer-Verlag | |

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 | |

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 |

## Conics |
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Kreise und Quadrate modulo p | Mathem. Semesterberichte 47 (2000), 51-73
| |

Conics: a Poor Man's Elliptic Curves | preprint | |

Higher Descent on Pell Conics I. From Legendre to Selmer | preprint | |

Higher Descent on Pell Conics II. Two Centuries of Missed Opportunities | draft | |

Higher Descent on Pell Conics III. The First $2$-Descent | draft | |

Simple counterexamples to the Local-Global principle (with W. Aitken) | draft | |

Euler's Trick and second 2-descents (with Ö. Öztürün) | draft | |

The Pell Equation | webliography up to 1945 | html |

## The Rest |
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Small norms in a quadratic field; an introductory section to the paper on simplest cubic fields that was omitted in the published version | unpublished | |

On Simplest Cubic Fields (with A. Pethö); | Manuscripta Math. 88 (1995), 53--58
| |

The Snake Lemma (new version Nov. 2002) | unpublished | |

Unsolved problems in Algebraic Number Theory | unpublished | |

## Translations of some articles |
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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). | |

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). | |

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) | |

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) | |

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. | |

Guy Henniart: The congruent number problem and its connections with elliptic curves and modular forms. | some journal of the SMF ? | |

Koch: Über den 2-Klassenkörperturm eines quadratischen Zahlkörpers | J. Reine Angew. Math. 214/215 (1964), 201--206. | |

Hasse: Vorlesungen über Klassenkörpertheorie. Teil I. Galois Theory | Physica Verlag Würzburg |

Last update: September 10, 2003