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Marie-France VIGNERAS (1981/1982)

Seminaire de Théorie des Nombres de Bordeaux

-invariants and Darmon cycles attached to modular forms

Victor Rotger, Marco Adamo Seveso (2012)

Journal of the European Mathematical Society

Let f be a modular eigenform of even weight k 2 and new at a prime p dividing exactly the level with respect to an indefinite quaternion algebra. The theory of Fontaine-Mazur allows to attach to f a monodromy module D f F M and an -invariant f F M . The first goal of this paper is building a suitable p -adic integration theory that allows us to construct a new monodromy module D f and -invariant f , in the spirit of Darmon. The two monodromy modules are isomorphic, and in particular the two -invariants are equal....

𝒟 -modules arithmétiques surcohérents. Application aux fonctions L

Daniel Caro (2004)

Annales de l’institut Fourier

Nous étudions d’abord le foncteur cohomologique local. Ensuite, nous introduisons la notion de 𝒟 -modules arithmétiques surcohérents. Nous prouvons que les F - isocristaux unités sont surcohérents et surtout que la surcohérence est stable par images directes, images inverses extraordinaires et foncteurs cohomologiques locaux. On obtient, via cette stabilité, une formule cohomologique pour les fonctions L associées aux complexes duaux de complexes surcohérents. Celle-ci étend celle d’Étesse et Le Stum...

0 - 1 sequences having the same numbers of ( 1 - 1 ) -couples of given distances

Antonín Lešanovský, Jan Rataj, Stanislav Hojek (1992)

Mathematica Bohemica

Let a be a 0 - 1 sequence with a finite number of terms equal to 1. The distance sequence δ ( a ) of a is defined as a sequence of the numbers of ( 1 - 1 ) -couples of given distances. The paper investigates such pairs of 0 - 1 sequences a , b that a is different from b and δ ( a ) = δ ( b ) .

1093

Paulo Ribenboim (2003)

Bollettino dell'Unione Matematica Italiana

.121221222... is not quadratic.

Florian Luca (2005)

Revista Matemática Complutense

In this note, we show that if b > 1 is an integer, f(X) ∈ Q[X] is an integer valued quadratic polynomial and K > 0 is any constant, then the b-adic number ∑n≥0 (an / bf(n)), where an ∈ Z and 1 ≤ |an| ≤ K for all n ≥ 0, is neither rational nor quadratic.

2 -modular lattices from ternary codes

Robin Chapman, Steven T. Dougherty, Philippe Gaborit, Patrick Solé (2002)

Journal de théorie des nombres de Bordeaux

The alphabet 𝐅 3 + v 𝐅 3 where v 2 = 1 is viewed here as a quotient of the ring of integers of 𝐐 ( - 2 ) by the ideal (3). Self-dual 𝐅 3 + v 𝐅 3 codes for the hermitian scalar product give 2 -modular lattices by construction A K . There is a Gray map which maps self-dual codes for the Euclidean scalar product into Type III codes with a fixed point free involution in their automorphism group. Gleason type theorems for the symmetrized weight enumerators of Euclidean self-dual codes and the length weight enumerator of hermitian self-dual...

2-Cohomology of semi-simple simply connected group-schemes over curves defined over p -adic fields

Jean-Claude Douai (2013)

Journal de Théorie des Nombres de Bordeaux

Let X be a proper, smooth, geometrically connected curve over a p -adic field k . Lichtenbaum proved that there exists a perfect duality: Br ( X ) × Pic ( X ) / between the Brauer and the Picard group of X , from which he deduced the existence of an injection of Br ( X ) in P X Br ( k P ) where P X and k P denotes the residual field of the point P . The aim of this paper is to prove that if G = G ˜ is an X e t - scheme of semi-simple simply connected groups (s.s.s.c groups), then we can deduce from Lichtenbaum’s results the neutrality of every X e t -gerb which...

3-Selmer groups for curves y 2 = x 3 + a

Andrea Bandini (2008)

Czechoslovak Mathematical Journal

We explicitly perform some steps of a 3-descent algorithm for the curves y 2 = x 3 + a , a a nonzero integer. In general this will enable us to bound the order of the 3-Selmer group of such curves.

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