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...
Central and genus class fields and the Hasse norm theorem
Central extensions and reciprocity laws
Certain L-functions at s = 1/2
Introduction. The vanishing orders of L-functions at the centers of their functional equations are interesting objects to study as one sees, for example, from the Birch-Swinnerton-Dyer conjecture on the Hasse-Weil L-functions associated with elliptic curves over number fields. In this paper we study the central zeros of the following types of L-functions: (i) the derivatives of the Mellin transforms of Hecke eigenforms for SL₂(ℤ), (ii) the Rankin-Selberg...
Chains of factorizations in orders of global fields
Changement du corps de base pour les représentations de
Character coordinates and annihilators of cyclotomic numbers.
Character Sums and Primitive Roots in Algebraic Number Fields.
Characteristic Classes of Kuga Fiber Varieties of Quaternion Type.
Characterization of irreducible algebraic integers by their norms
Charakerisierung der lokalbeschränkten Ringtopologien auf globalen Körpern.
Chebotarev formations and quantitative aspects of non-unique factorizations
Chebotarev sets
We consider the problem of determining whether a set of primes, or, more generally, prime ideals in a number field, can be realized as a finite union of residue classes, or of Frobenius conjugacy classes. We give necessary conditions for a set to be realized in this manner, and show that the subset of primes consisting of every other prime cannot be expressed in this way, even if we allow a finite number of exceptions.
Chebyshev's bias.
Chebyshev's method for number fields
We give an elementary proof of an explicit estimate for the number of primes splitting completely in an extension of the rationals. The proof uses binomial coefficents and extends Chebyshev's classical approach.
Chen's theorem in totally real algebraic number fields
Chern classes, adeles and L-functions.
Chern classes of group representations over a number field
Chern numbers of cusp resolutions in totally real cubic number fields.