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| unpublished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| unpublished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 |
Historical |
| 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 |
Conics |
| 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 |