A New Minor-Arcs Estimate for Number Fields

  • Morley Davidson
Part of the Mathematics and Its Applications book series (MAIA, volume 467)


We re-examine Körner’s number field version of a minor-arcs estimate introduced by Vinogradov into the study of Waring’s function G(k). Dependencies on both k and the degree n of the number field are reduced via improved mean value estimates for Weyl sums over ‘smooth’ algebraic integers.


Number Field Class Number Algebraic Integer Prime Number Theorem Algebraic Number Field 
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Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Morley Davidson
    • 1
  1. 1.Dept. of Mathematics and Computer ScienceKent State UniversityKentUSA

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