Generalized Analytic Automorphic Forms in Hypercomplex Spaces

Kraußhar, Rolf Sören

doi:10.1007/b95203

Cited by 51 publications

(137 citation statements)

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“…However, as shown in [23], even in the monogenic case, the absolute convergence abscissa with respect to the generalized modular group of these generalized Eisenstein series is only p < n − 2. Here we overcome this convergence problem for the cases p = n − 2 and p = n − 1 by adapting a classical trick of Hecke, mentioned for example in [18].…”

Section: Introductionmentioning

confidence: 91%

“…To introduce these types of Eisenstein series we shall need the following convergence lemma which is proved in [23]. Now following [23] we introduce the following generalized Eisenstein series.…”

Section: More Precisely This Bundle Is Constructed Overmentioning

confidence: 99%

“…Now following [23] we introduce the following generalized Eisenstein series. One can directly verify by a rearrangement argument, [23], that the Series (5) satisfies the transformation rule…”

Section: More Precisely This Bundle Is Constructed Overmentioning

confidence: 99%

“…Further one can combine the arguments used to establish Proposition 7 with arguments presented in [23] to obtain Proposition 8 The series…”

Section: Theorem 1 (Cauchy's Integral Formula Formentioning

confidence: 99%

See 3 more Smart Citations

Dirac type operators for spin manifolds associated to congruence subgroups of generalized modular groups

Bulla

Constales

Kraußhar

et al. 2010

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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Section: Introductionmentioning

confidence: 91%

Section: More Precisely This Bundle Is Constructed Overmentioning

confidence: 99%

Section: More Precisely This Bundle Is Constructed Overmentioning

confidence: 99%

“…Further one can combine the arguments used to establish Proposition 7 with arguments presented in [23] to obtain Proposition 8 The series…”

Section: Theorem 1 (Cauchy's Integral Formula Formentioning

confidence: 99%

See 2 more Smart Citations

Dirac type operators for spin manifolds associated to congruence subgroups of generalized modular groups

Bulla

Constales

Kraußhar

et al. 2010

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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“…The recent development of the theory of monogenic automorphic forms [5] gave new some impulses in the direction of obtaining explicit formulas for the Bergman kernel functions for a larger class of domains.…”

Section: Introductionmentioning

confidence: 99%

Bergman spaces of higher‐dimensional hyperbolic polyhedron‐type domains I

Constales

Kraußhar

2005

Math Methods in App Sciences

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A faster numerical scheme for a coupled system modeling soil erosion and sediment transport

Cordier

Lucas

2015

Water Resources Research

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Overland flow and soil erosion play an essential role in water quality and soil degradation.Such processes, involving the interactions between water flow and the bed sediment, are classically described by a well-established system coupling the shallow water equations and the Hairsine-Rose model. Numerical approximation of this coupled system requires advanced methods to preserve some important physical and mathematical properties; in particular, the steady states and the positivity of both water depth and sediment concentration. Recently, finite volume schemes based on Roe's solver have been proposed by Heng et al. (2009) and Kim et al. (2013) for one and two-dimensional problems. In their approach, an additional and artificial restriction on the time step is required to guarantee the positivity of sediment concentration. This artificial condition can lead the computation to be costly when dealing with very shallow flow and wet/dry fronts. The main result of this paper is to propose a new and faster scheme for which only the CFL condition of the shallow water equations is sufficient to preserve the positivity of sediment concentration. In addition, the numerical procedure of the erosion part can be used with any well-balanced and positivity preserving scheme of the shallow water equations. The proposed method is tested on classical benchmarks and also on a realistic configuration.

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Generalized Analytic Automorphic Forms in Hypercomplex Spaces

Cited by 51 publications

References 0 publications

Dirac type operators for spin manifolds associated to congruence subgroups of generalized modular groups

Dirac type operators for spin manifolds associated to congruence subgroups of generalized modular groups

Bergman spaces of higher‐dimensional hyperbolic polyhedron‐type domains I

A faster numerical scheme for a coupled system modeling soil erosion and sediment transport

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