Articles

Since my submission rights to the arxiv were removed recently for having committed the crime of submitting a note on the normality of Hilbert class fields without a single reference, the latest versions of my articles can, for the time being, be found here.

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 arxiv
Class groups of cyclotomic number fields II Acta Arith. 84 (1998), 59-70 arxiv
Class groups of cyclotomic number fields III Acta Arith. 131 (2008), 255-266 arxiv
The 4-class group of real quadratic number fields unpublished arxiv
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 arxiv
Class Groups of Dihedral Extensions Math. Nachr 278 (2005), 679-691 arxiv
Why is the class number of Q(11^(1/3)) even? Bohemian J. Math. 138 (2013), No. 2, 149-163 arxiv
Binomial Squares in Pure Cubic Number Fields J. Theor. Nombres Bordeaux 24 (2012), 691-704 arxiv
Relations in the 2-Class Group of Quadratic Number Fields J. Austral. Math. Soc. 93 (2012), 115-120 arxiv
Simerka - Quadratic Forms and Factorization LMS J. Comput. Math. 16 (2013), 118--129 arxiv
The Ambiguous Class Number Formula Revisited J. of the Ramanujan Math. Soc. 415-421 arxiv

Reciprocity Laws

Rational Quartic Reciprocity Acta Arith. 67 (1994), 387--390 arxiv
Rational Quartic Reciprocity II Acta Arith. 80 (1997), 273--276 arxiv
Reciprocity Laws. From Euler to Eisenstein Springer Verlag html
A Supplement to Scholz's reciprocity law Acta Arith. 129 (2007), 319--324 arxiv
Harbingers of Artin's reciprocity law I. The Continuing Story of Auxiliary Primes unpublished arxiv
Harbingers of Artin's reciprocity law II. Irreducibility of Cyclotomic Polynomials unpublished arxiv
Harbingers of Artin's reciprocity law III. Gauss's Lemma and Artin's Transfer unpublished arxiv
Harbingers of Artin's reciprocity law IV. Bernstein's Reciprocity Law unpublished arxiv
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 arxiv
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 arxiv
Quartic Euclidean Number Fields unpublished arxiv
An Application of the Dedekind-Hasse Criterion unpublished arxiv
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 arxiv
Imaginary quadratic number fields with cyclic Cl2(k1) (with Elliot 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 arxiv
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 Elliot Benjamin and C. Snyder) J. Number Theory 103 (2003), 38-70 pdf
A survey on Class Field Towers www pdf
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 Abh. Math. Sem. Hamburg 2007 arxiv
Kronecker-Weber via Stickelberger J. Théor. Nombres Bordeaux 17 (2005), 579--582 arxiv
On the unit group of some multiquadratic number fields (with E. Benjamin, C. Snyder) Pac. J. Math. 230 (2007), 27-40 pdf
Grün's theorems and class groups Arch. Math. 96 (2011), 135-138 arxiv
Hilbert 2-Class Fields and 2-Descent preprint arxiv
On the Normality of Hilbert Class Fields preprint pdf

Elliptic Curves

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

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
Helmut Hasse und Emmy Noether. Die Korrespondenz 1925--1935 (with P. Roquette) Universitätsverlag Göttingen 2006 html
Jacobis Vorlesungen über Zahlentheorie aus dem Wintersemester 1836/37 (with H. Pieper) Algorismus 62, Rauner Verlag Augsburg 2007 html
Emil Artin und Helmut Hasse. Die Korrespondenz 1923 -- 1934. G. Frei, P. Roquette, unter Mitwirkung von F. Lemmermeyer Universitätsverlag Göttingen 2006 html
Zur Zahlentheorie der Griechen I: Euklids Fundamentalsatz der Arithmetik Math. Semesterberichte 55 (2008), 181-195 pdf
Zur Zahlentheorie der Griechen II: Gauss'sche Lemmas und Rieszsche Ringe Math. Semesterberichte 56 (2009), 39-51 pdf
Jacobi and Kummer's ideal numbers Abh. Math. Sem. Hamburg 79 (2009), 165-187 arxiv
Euler, Goldbach, and "Fermat's Theorem" Elem. Math. 2010 arxiv
Die mathematischen Tagebücher von Hasse 1923-1935 Universitätsverlag Göttingen 2013 html
Leonardo da Vinci's Proof of the Theorem of Pythagoras Coll. J. Math. pdf
Emil Artin and Helmut Hasse. The Correspondence 1923 -- 1934. G. Frei, F. Lemmermeyer, P. Roquette, Springer 2014 html pdf
The Correspondence Euler - Goldbach (with M. Mattmüller) Euler's Opera Omnia, Series IV-A.4 (2014) html
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 and Affine Algebraic Varieties

Kreise und Quadrate modulo p Mathem. Semesterberichte 47 (2000), 51-73 pdf
Conics: a Poor Man's Elliptic Curves preprint arxiv
Higher Descent on Pell Conics I. From Legendre to Selmer preprint arxiv
Higher Descent on Pell Conics II. Two Centuries of Missed Opportunities preprint arxiv
Higher Descent on Pell Conics III. The First $2$-Descent preprint arxiv
Counterexamples to the Hasse principle: An Elementary Introduction (with W. Aitken) Amer. Math. Monthly 118 (2011), 610-628 arxiv
Arithmetic of Pell Surfaces (with S. Hambleton) Acta Arithmetica 146 (2011), 1-12 arxiv
Modular Pell conics preprint pdf
Parametrization of Algebraic Curves from a number theorist's point of view. Amer. Math. Mon. 119 (2012), 573-583 arxiv
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 arxiv
On Simplest Cubic Fields (with A. Pethö); Manuscripta Math. 88 (1995), 53--58 arxiv
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: May 2014