Title: On a new type of Eisenstein series in Clifford analysis
Authors: Krausshar, Rolf Sören # ×
Issue Date: 2001
Publisher: Heldermann Verlag
Series Title: Zeitschrift für Analysis und ihre Anwendungen vol:20 issue:4 pages:1007-1029
Abstract: In this paper we deduce a recursion formula for the partial derivatives of the fundamental solution of the generalized Cauchy-Riemann operator in $R^{k+1}$ in terms of permutational products. These functions generalize the classical negative power functions to Clifford analysis. We exploit them to introduce a new generalization of the classical complex analytic Eisenstein series on the half-plane to higher dimensions satisfying the generalized Cauchy-Riemann differential equation. Under function theoretical and number theoretical aspects we investigate their Fourier series expansion in which multiple divisor sums and certain generalizations of the Riemann-Zeta function play a crucial role.
Description: Impactfactor 2007: 0.641
ISSN: 0232-2064
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Analysis Section
× corresponding author
# (joint) last author

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