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Title: Eisenstein Series in Clifford Analysis
Authors: Krausshar, Rolf Sören
Editors: Bock, H. H.
Jongen, H. Th.
Plesken, W.
Issue Date: 2000
Publisher: Wissenschaftsverlag Mainz in Aachen
Series Title: Aachener Beitrage zur Mathematik vol:28
Abstract: In this book we deal with generalizations of the classical Eisenstein series in hypercomplex function theory including the property of monogenicity.
They admit a construction of monogenic generalizations of the classical tangent, cotangent, secant and cosecant function and the elliptic functions. We study properties of them and characterize them by certain duplication formulas and their principal parts.
Furthermore, the Laurent expansions of these functions are investigated. They lead to a generalization of another type of classical Eisenstein series being $k$-fold periodic and left and right monogenic in a half-space of $\mathbb{R}^{k+1}$. We determine the Fourier series expansion and discuss number theoretical aspects related with them, e.g., divisor sums and generalized Riemann-Zeta functions.
ISBN: 3-86073-648-5
Publication status: published
KU Leuven publication type: IBa
Appears in Collections:Analysis Section

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