Displaying similar documents to “The Behavior of Rigid Analytic Functions Around Orbits of Elements of < > ℂ p < >”

On p -adic Euler constants

Abhishek Bharadwaj (2021)

Czechoslovak Mathematical Journal

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The goal of this article is to associate a p -adic analytic function to the Euler constants γ p ( a , F ) , study the properties of these functions in the neighborhood of s = 1 and introduce a p -adic analogue of the infinite sum ∑ n ≥ 1 f ( n ) / n for an algebraic valued, periodic function f . After this, we prove the theorem of Baker, Birch and Wirsing in this setup and discuss irrationality results associated to p -adic Euler constants generalising the earlier known results in this direction. Finally, we define and prove...

The Heyde theorem on a-adic solenoids

Margaryta Myronyuk (2013)

Colloquium Mathematicae

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We prove the following analogue of the Heyde theorem for a-adic solenoids. Let ξ₁, ξ₂ be independent random variables with values in an a-adic solenoid Σ a and with distributions μ₁, μ₂. Let α j , β j be topological automorphisms of Σ a such that β ₁ α - 1 ₁ ± β ₂ α - 1 ₂ are topological automorphisms of Σ a too. Assuming that the conditional distribution of the linear form L₂ = β₁ξ₁ + β₂ξ₂ given L₁ = α₁ξ₁ + α₂ξ₂ is symmetric, we describe the possible distributions μ₁, μ₂.

Maximum modulus in a bidisc of analytic functions of bounded 𝐋 -index and an analogue of Hayman’s theorem

Andriy Bandura, Nataliia Petrechko, Oleh Skaskiv (2018)

Mathematica Bohemica

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We generalize some criteria of boundedness of 𝐋 -index in joint variables for in a bidisc analytic functions. Our propositions give an estimate the maximum modulus on a skeleton in a bidisc and an estimate of ( p + 1 ) th partial derivative by lower order partial derivatives (analogue of Hayman’s theorem).

Persistence of fixed points under rigid perturbations of maps

Salvador Addas-Zanata, Pedro A. S. Salomão (2014)

Fundamenta Mathematicae

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Let f: S¹ × [0,1] → S¹ × [0,1] be a real-analytic diffeomorphism which is homotopic to the identity map and preserves an area form. Assume that for some lift f̃: ℝ × [0,1] → ℝ × [0,1] we have Fix(f̃) = ℝ × 0 and that f̃ positively translates points in ℝ × 1. Let f ̃ ϵ be the perturbation of f̃ by the rigid horizontal translation (x,y) ↦ (x+ϵ,y). We show that F i x ( f ̃ ϵ ) = ∅ for all ϵ > 0 sufficiently small. The proof follows from Kerékjártó’s construction of Brouwer lines for orientation preserving...

Base change for Bernstein centers of depth zero principal series blocks

Thomas J. Haines (2012)

Annales scientifiques de l'École Normale Supérieure

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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].

On the quasi-periodic p -adic Ruban continued fractions

Basma Ammous, Nour Ben Mahmoud, Mohamed Hbaib (2022)

Czechoslovak Mathematical Journal

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We study a family of quasi periodic p -adic Ruban continued fractions in the p -adic field ℚ p and we give a criterion of a quadratic or transcendental p -adic number which based on the p -adic version of the subspace theorem due to Schlickewei.

An explicit computation of p -stabilized vectors

Michitaka MIYAUCHI, Takuya YAMAUCHI (2014)

Journal de Théorie des Nombres de Bordeaux

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In this paper, we give a concrete method to compute p -stabilized vectors in the space of parahori-fixed vectors for connected reductive groups over p -adic fields. An application to the global setting is also discussed. In particular, we give an explicit p -stabilized form of a Saito-Kurokawa lift.

On certain subclasses of analytic functions associated with the Carlson–Shaffer operator

Jagannath Patel, Ashok Kumar Sahoo (2014)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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The object of the present paper is to solve Fekete-Szego problem and determine the sharp upper bound to the second Hankel determinant for a certain class R λ ( a , c , A , B ) of analytic functions in the unit disk. We also investigate several majorization properties for functions belonging to a subclass R ˜ λ ( a , c , A , B ) of R λ ( a , c , A , B ) and related function classes. Relevant connections of the main results obtained here with those given by earlier workers on the subject are pointed out.

Solutions of non-homogeneous linear differential equations in the unit disc

Ting-Bin Cao, Zhong-Shu Deng (2010)

Annales Polonici Mathematici

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The main purpose of this paper is to consider the analytic solutions of the non-homogeneous linear differential equation f ( k ) + a k - 1 ( z ) f ( k - 1 ) + ⋯ + a ₁ ( z ) f ' + a ₀ ( z ) f = F ( z ) , where all coefficients a ₀ , a ₁ , . . . , a k - 1 , F ≢ 0 are analytic functions in the unit disc = z∈ℂ: |z|<1. We obtain some results classifying the growth of finite iterated order solutions in terms of the coefficients with finite iterated type. The convergence exponents of zeros and fixed points of solutions are also investigated.

Lifting the field of norms

Laurent Berger (2014)

Journal de l’École polytechnique — Mathématiques

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Let K be a finite extension of Q p . The field of norms of a p -adic Lie extension K ∞ / K is a local field of characteristic p which comes equipped with an action of Gal ( K ∞ / K ) . When can we lift this action to characteristic 0 , along with a compatible Frobenius map? In this note, we formulate precisely this question, explain its relevance to the theory of ( ϕ , Γ ) -modules, and give a condition for the existence of certain types of lifts.

Algebraic and analytic properties of solutions of abstract differential equations

R. Bittner

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CONTENTSINTRODUCTION............................................................................................................................... 3Chapter I. ALGEBRAIC PROPERTIES OF SOLUTIONS OF ABSTRACT DIFFERENTIALEQUATIONS§ 1. Ordinary abstract differential equations1. Taylor’s formula for an abstract derivative.......................................................................... 42 π-solutions....................................................................................................................................

An alternative description of the Drinfeld p -adic half-plane

Stephen Kudla, Michael Rapoport (2014)

Annales de l’institut Fourier

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We show that the Deligne formal model of the Drinfeld p -adic half-plane relative to a local field F represents a moduli problem of polarized O F -modules with an action of the ring of integers in a quadratic extension E of F . The proof proceeds by establishing a comparison isomorphism with the Drinfeld moduli problem. This isomorphism reflects the accidental isomorphism of SL 2 ( F ) and SU ( C ) ( F ) for a two-dimensional split hermitian space C for E / F .