Science in China Series A: Mathematics

, Volume 44, Issue 8, pp 1003–1015

Upper bounds on a two-term exponential sum*

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Abstract

We obtain upper bounds for mixed exponential sums of the type\(S(\chi ,f,p^m ) = \sum\nolimits_{x = 1}^{p^n } {\chi (x)e} _{p^m } (ax^n + bx)\) where pm is a prime power with m⩾ 2 and X is a multiplicative character (mod pm). If X is primitive or p⫮(a, b) then we obtain |S(χ,f,pm)| ⩽2np2/3 m. If X is of conductor p and p⫮( a, b) then we get the stronger bound |S(χ,f,pm)|⩽npm/2.

Keywords

exponential sums primitive character weil’sbound 

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Copyright information

© Science in China Press 2001

Authors and Affiliations

  1. 1.Department of MathematicsKansas State UniversityManhattanUSA
  2. 2.Department of MathematicsTsinghua UniversityBeijingChina

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