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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 821949, 9 pages
http://dx.doi.org/10.1155/2012/821949
Research Article

Dirichlet Characters, Gauss Sums, and Inverse Z Transform

1Department of Mathematical Sciences, Xi'an Jiaotong University, Xi'an, Shaanxi, China
2Department of Mathematics, Northwest University, Xi'an, Shaanxi, China

Received 26 December 2011; Accepted 9 January 2012

Academic Editor: Karl Joachim Wirths

Copyright © 2012 Jing Gao and Huaning Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A generalized Möbius transform is presented. It is based on Dirichlet characters. A general algorithm is developed to compute the inverse transform on the unit circle, and an error estimate is given for the truncated series representation.