Arithmetic of formal groups and applications I: Universal norm subgroups.
Arithmetik in Frobeniuserweiterungen.
Arithmétique des courbes elliptiques et théorie d'Iwasawa
Artin L-functions and modular forms associated to quasi-cyclotomic fields
Artin-Root Numbers and Normal Integral Bases for Quaternion Fields.
Aspects numériques de la détermination du l-groupe des classes d'idéaux des extensions cycliques de degré premier l
Bases for cyclotomic units
Bases normales d'entiers dans les extensions de Kummer de degré premier
Si est un corps de nombres, on note son anneau d’entiers ; si est une extension galoisienne finie de corps de nombres de groupe de Galois , on appelle base normale de sur toute base de en tant que -module de la forme avec . On démontre dans ce travail un critère d’existence de base normale d’entiers pour les extensions de Kummer de degré premier, qui permet une construction explicite en cas d’existence ; les principaux outils pour la démonstration sont une formule de Fröhlich pour...
Bases normales, unités et conjecture faible de Leopoldt.
Beitrag zur Theorie gewisser complexer Zahlen.
Bernoulli numbers, Hurwitz numbers, p-adic L-functions and Kummer's criterion.
Let K = Q(ζp) and let hp be its class number. Kummer showed that p divides hp if and only if p divides the numerator of some Bernoulli number. In this expository note we discuss the generalizations of this type of criterion to totally real fields and quadratic imaginary fields.
Bicyclotomic polynomials and impossible intersections
In a recent paper we proved that there are at most finitely many complex numbers such that the points and are both torsion on the Legendre elliptic curve defined by . In a sequel we gave a generalization to any two points with coordinates algebraic over the field and even over . Here we reconsider the special case and with complex numbers and .
Brumer-Stark-Stickelberger
Catalan without logarithmic forms (after Bugeaud, Hanrot and Mihăilescu)
This is an exposition of the recent work of Bugeaud, Hanrot and Mihăilescu showing that Catalan’s conjecture can be proved without using logarithmic forms and electronic computations.
Catalanova domněnka dokázána
Catalan’s conjecture
The subject of the talk is the recent work of Mihăilescu, who proved that the equation has no solutions in non-zero integers and odd primes . Together with the results of Lebesgue (1850) and Ko Chao (1865) this implies the celebratedconjecture of Catalan (1843): the only solution to in integers and is . Before the work of Mihăilescu the most definitive result on Catalan’s problem was due to Tijdeman (1976), who proved that the solutions of Catalan’s equation are bounded by an absolute...
Character coordinates and annihilators of cyclotomic numbers.
Chern classes of group representations over a number field
Class group of a cyclotomic -extension
Class Group Rank Relations in Zl-Extensions.