Science in China Series A: Mathematics

, Volume 44, Issue 8, pp 1003–1015

Upper bounds on a two-term exponential sum*

Article

DOI: 10.1007/BF02878976

Cite this article as:
Cochrane, T. & Zheng, Z. Sci. China Ser. A-Math. (2001) 44: 1003. doi:10.1007/BF02878976

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 sumsprimitive characterweil’sbound

Copyright information

© Science in China Press 2001

Authors and Affiliations

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