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A Penultimate Step toward Cubic Theta-Weyl Sums

  • Yoshinobu Nakai
Part of the Developments in Mathematics book series (DEVM, volume 8)

Abstract

The attempt at interpreting the Weyl sums as finite theta series (theta-Weyl sums) has been successful only in the case of quadratic polynomials. In this paper we shall present basic ingredients for interpreting cubic Weyl sums as finite theta series, i.e. the cubic continued fraction expansion, the van der Corput reciprocal function, cubic reciprocal and parabolic transformations.

Keywords

Weyl sum exponential sum cubic continued fraction expansion Diophantine approximation van der Corput reciprocal function 

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Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • Yoshinobu Nakai
    • 1
  1. 1.Department of Mathematics, Faculty of EducationYamanashi UniversityKofu, YamanashiJapan

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