Displaying similar documents to “On computing Belyi maps”

Gauss–Manin connections for p -adic families of nearly overconvergent modular forms

Robert Harron, Liang Xiao (2014)

Annales de l’institut Fourier

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We interpolate the Gauss–Manin connection in p -adic families of nearly overconvergent modular forms. This gives a family of Maass–Shimura type differential operators from the space of nearly overconvergent modular forms of type r to the space of nearly overconvergent modular forms of type r + 1 with p -adic weight shifted by 2 . Our construction is purely geometric, using Andreatta–Iovita–Stevens and Pilloni’s geometric construction of eigencurves, and should thus generalize to higher rank...

Overconvergent modular symbols and p -adic L -functions

Robert Pollack, Glenn Stevens (2011)

Annales scientifiques de l'École Normale Supérieure

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This paper is a constructive investigation of the relationship between classical modular symbols and overconvergent p -adic modular symbols. Specifically, we give a constructive proof of a (Theorem 1.1) due to the second author [19] proving existence and uniqueness of overconvergent eigenliftings of classical modular eigensymbols of . As an application we describe a polynomial-time algorithm for explicit computation of associated p -adic L -functions in this case. In the case of, the control...

Parapuzzle of the multibrot set and typical dynamics of unimodal maps

Artur Avila, Mikhail Lyubich, Weixiao Shen (2011)

Journal of the European Mathematical Society

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We study the parameter space of unicritical polynomials f c : z z d + c . For complex parameters, we prove that for Lebesgue almost every c , the map f c is either hyperbolic or infinitely renormalizable. For real parameters, we prove that for Lebesgue almost every c , the map f c is either hyperbolic, or Collet–Eckmann, or infinitely renormalizable. These results are based on controlling the spacing between consecutive elements in the “principal nest” of parapuzzle pieces.

On the Euler Function on Differences Between the Coordinates of Points on Modular Hyperbolas

Igor E. Shparlinski (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

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For a prime p > 2, an integer a with gcd(a,p) = 1 and real 1 ≤ X,Y < p, we consider the set of points on the modular hyperbola a , p ( X , Y ) = ( x , y ) : x y a ( m o d p ) , 1 x X , 1 y Y . We give asymptotic formulas for the average values ( x , y ) a , p ( X , Y ) x y * φ ( | x - y | ) / | x - y | and ( x , y ) a , p ( X , X ) x y * φ ( | x - y | ) with the Euler function φ(k) on the differences between the components of points of a , p ( X , Y ) .

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 α - 1 ± β α - 1 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.

Iwasawa theory for symmetric powers of CM modular forms at non-ordinary primes

Robert Harron, Antonio Lei (2014)

Journal de Théorie des Nombres de Bordeaux

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Let f be a cuspidal newform with complex multiplication (CM) and let p be an odd prime at which f is non-ordinary. We construct admissible p -adic L -functions for the symmetric powers of f , thus verifying conjectures of Dabrowski and Panchishkin in this special case. We combine this with recent work of Benois to prove the trivial zero conjecture in this setting. We also construct “mixed” plus and minus p -adic L -functions and prove an analogue of Pollack’s decomposition of the admissible...

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 automatic boundedness of Nemytskiĭ set-valued operators

S. Rolewicz, Wen Song (1995)

Studia Mathematica

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Let X, Y be two separable F-spaces. Let (Ω,Σ,μ) be a measure space with μ complete, non-atomic and σ-finite. Let N F be the Nemytskiĭ set-valued operator induced by a sup-measurable set-valued function F : Ω × X 2 Y . It is shown that if N F maps a modular space ( N ( L ( Ω , Σ , μ ; X ) ) , ϱ N , μ ) into subsets of a modular space ( M ( L ( Ω , Σ , μ ; Y ) ) , ϱ M , μ ) , then N F is automatically modular bounded, i.e. for each set K ⊂ N(L(Ω,Σ,μ;X)) such that r K = s u p ϱ N , μ ( x ) : x K < we have s u p ϱ M , μ ( y ) : y N F ( K ) < .

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...

Some remarks providing discontinuous maps on some C p ( X ) spaces

S. Moll (2008)

Banach Center Publications

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Let X be a completely regular Hausdorff topological space and C p ( X ) the space of continuous real-valued maps on X endowed with the pointwise topology. A simple and natural argument is presented to show how to construct on the space C p ( X ) , if X contains a homeomorphic copy of the closed interval [0,1], real-valued maps which are everywhere discontinuous but continuous on all compact subsets of C p ( X ) .

On the de Rham and p -adic realizations of the elliptic polylogarithm for CM elliptic curves

Kenichi Bannai, Shinichi Kobayashi, Takeshi Tsuji (2010)

Annales scientifiques de l'École Normale Supérieure

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In this paper, we give an explicit description of the de Rham and p -adic polylogarithms for elliptic curves using the Kronecker theta function. In particular, consider an elliptic curve E defined over an imaginary quadratic field 𝕂 with complex multiplication by the full ring of integers 𝒪 𝕂 of 𝕂 . Note that our condition implies that 𝕂 has class number one. Assume in addition that E has good reduction above a prime p 5 unramified in 𝒪 𝕂 . In this case, we prove that the specializations of the...

Local Indecomposability of Hilbert Modular Galois Representations

Bin Zhao (2014)

Annales de l’institut Fourier

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We prove the indecomposability of the Galois representation restricted to the p -decomposition group attached to a non CM nearly p -ordinary weight two Hilbert modular form over a totally real field F under the assumption that either the degree of F over is odd or the automorphic representation attached to the Hilbert modular form is square integrable at some finite place of F .