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Linear relations between modular forms for Г 0 + (p)

SoYoung Choi, Chang Heon Kim (2015)

Open Mathematics

We find linear relations among the Fourier coefficients of modular forms for the group Г0+(p) of genus zero. As an application of these linear relations, we derive congruence relations satisfied by the Fourier coefficients of normalized Hecke eigenforms.

Linearly invariant families of holomorphic functions in the unit polydisc

Janusz Godula, Victor Starkov (1996)

Banach Center Publications

In this paper we extend the definition of the linearly invariant family and the definition of the universal linearly invariant family to higher dimensional case. We characterize these classes and give some of their properties. We also give a relationship of these families with the Bloch space.

Linearly-invariant families and generalized Meixner–Pollaczek polynomials

Iwona Naraniecka, Jan Szynal, Anna Tatarczak (2013)

Annales UMCS, Mathematica

The extremal functions f0(z) realizing the maxima of some functionals (e.g. max |a3|, and max arg f′(z)) within the so-called universal linearly invariant family Uα (in the sense of Pommerenke [10]) have such a form that f′0(z) looks similar to generating function for Meixner-Pollaczek (MP) polynomials [2], [8]. This fact gives motivation for the definition and study of the generalized Meixner-Pollaczek (GMP) polynomials Pλn (x; θ,ψ) of a real variable x as coefficients of [###] where the parameters...

Liouville type theorems for mappings with bounded (co)-distortion

Marc Troyanov, Sergei Vodop'yanov (2002)

Annales de l’institut Fourier

We obtain Liouville type theorems for mappings with bounded s -distorsion between Riemannian manifolds. Besides these mappings, we introduce and study a new class, which we call mappings with bounded q -codistorsion.

Lipschitz constants for a hyperbolic type metric under Möbius transformations

Yinping Wu, Gendi Wang, Gaili Jia, Xiaohui Zhang (2024)

Czechoslovak Mathematical Journal

Let D be a nonempty open set in a metric space ( X , d ) with D . Define h D , c ( x , y ) = log 1 + c d ( x , y ) d D ( x ) d D ( y ) , where d D ( x ) = d ( x , D ) is the distance from x to the boundary of D . For every c 2 , h D , c is a metric. We study the sharp Lipschitz constants for the metric h D , c under Möbius transformations of the unit ball, the upper half space, and the punctured unit ball.

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