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B dR -représentations dans le cas relatif

Fabrizio Andreatta, Olivier Brinon (2010)

Annales scientifiques de l'École Normale Supérieure

Dans ce travail nous développons un analogue relatif de la théorie de Sen pour les B dR -représentations. On donne des applications à la théorie des représentations p -adiques, en la reliant à la théorie des ( ϕ , Γ ) -modules relatifs, et à celle des modules de Higgs p -adiques développée par G. Faltings.

Badly approximable systems of linear forms over a field of formal series

Simon Kristensen (2006)

Journal de Théorie des Nombres de Bordeaux

We prove that the Hausdorff dimension of the set of badly approximable systems of m linear forms in n variables over the field of Laurent series with coefficients from a finite field is maximal. This is an analogue of Schmidt’s multi-dimensional generalisation of Jarník’s Theorem on badly approximable numbers.

Bad(s,t) is hyperplane absolute winning

Erez Nesharim, David Simmons (2014)

Acta Arithmetica

J. An proved that for any s,t ≥ 0 such that s + t = 1, Bad (s,t) is (34√2)¯¹-winning for Schmidt's game. We show that using the main lemma from [An] one can derive a stronger result, namely that Bad (s,t) is hyperplane absolute winning in the sense of [BFKRW]. As a consequence, one can deduce the full Hausdorff dimension of Bad (s,t) intersected with certain fractals.

Banach algebra techniques in the theory of arithmetic functions

Lutz G. Lucht (2008)

Acta Mathematica Universitatis Ostraviensis

For infinite discrete additive semigroups X ⊂ [ 0 , ∞ ) we study normed algebras of arithmetic functions g : X → ℂ endowed with the linear operations and the convolution. In particular, we investigate the problem of scaling the mean deviation of related multiplicative functions for X = log ℕ . This involves an extension of Banach algebras of arithmetic functions by introducing weight functions and proving a weighted inversion theorem of Wiener type in the frame of Gelfand’s theory of commutative Banach algebras.

Bartz-Marlewski equation with generalized Lucas components

Hayder R. Hashim (2022)

Archivum Mathematicum

Let { U n } = { U n ( P , Q ) } and { V n } = { V n ( P , Q ) } be the Lucas sequences of the first and second kind respectively at the parameters P ≥ 1 and Q ∈ { - 1 , 1 } . In this paper, we provide a technique for characterizing the solutions of the so-called Bartz-Marlewski equation x 2 - 3 x y + y 2 + x = 0 , where ( x , y ) = ( U i , U j ) or ( V i , V j ) with i , j ≥ 1 . Then, the procedure of this technique is applied to completely resolve this equation with certain values of such parameters.

Base change for Bernstein centers of depth zero principal series blocks

Thomas J. Haines (2012)

Annales scientifiques de l'École Normale Supérieure

Let  G be an unramified group over a p -adic field. This article introduces a base change homomorphism for Bernstein centers of depth-zero principal series blocks for  G and proves the corresponding base change fundamental lemma. This result is used in the approach to Shimura varieties with Γ 1 ( p ) -level structure initiated by M. Rapoport and the author in [15].

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