On the Mean Value of General $k$-th Gauss Sums
Received:February 25, 2010  Revised:May 26, 2011
Key Words: general Gauss sums   character sums   residue system   mean value.  
Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11071194) and the Northwest University Doctorate Dissertation of Excellence Funds (Grant No.09YYB05).
Author NameAffiliation
Yuan HE Department of Mathematics, Northwest University, Shaanxi $710127$, P. R. China
College of Mathematics and Software Science, Sichuan Normal University, Sichuan $610066$, P. R. China 
Qun Ying LIAO College of Mathematics and Software Science, Sichuan Normal University, Sichuan $610066$, P. R. China 
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Abstract:
      The main purpose of this paper is using residue system and character sums methods to investigate the mean value properties of general $k$-th Gauss sums, and two exact calculating formulas are given.
Citation:
DOI:10.3770/j.issn:1000-341X.2011.06.007
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