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Twisted exponential sums of polynomials in one variable

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Abstract

The twisted T-adic exponential sums associated to a polynomial in one variable are studied. An explicit arithmetic polygon in terms of the highest two exponents of the polynomial is proved to be a lower bound of the Newton polygon of the C-function of the twisted T-adic exponential sums. This bound gives lower bounds for the Newton polygon of the L-function of twisted p-power order exponential sums.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Jiao Tong University, Shanghai, 200240, China

    ChunLei Liu

  2. Department of Fundamental Subject, Tianjin Institute of Urban Construction, Tianjin, 300384, China

    WenXin Liu

  3. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

    WenXin Liu

Authors
  1. ChunLei Liu
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  2. WenXin Liu
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Correspondence to ChunLei Liu.

Additional information

Dedicated to Professor Wang Yuan on the Occasion of his 80th Birthday

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Liu, C., Liu, W. Twisted exponential sums of polynomials in one variable. Sci. China Math. 53, 2395–2404 (2010). https://doi.org/10.1007/s11425-010-3144-2

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  • DOI: https://doi.org/10.1007/s11425-010-3144-2

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