Chunlei Liu, Wenxin Liu, Chuanze Niu
Abstract
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The $T$-adic exponential sum associated to a Laurent polynomial in one variable is studied. An explicit arithmetic polygon is proved to be the generic Newton polygon of the $C$-function of the T-adic exponential sum. It gives the generic Newton polygon of $L$-functions of $p$-power order exponential sums.
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The $T$-adic exponential sum associated to a Laurent polynomial in one variable is studied. An explicit arithmetic polygon is proved to be the generic Newton polygon of the $C$-function of the T-adic exponential sum. It gives the generic Newton polygon of $L$-functions of $p$-power order exponential sums.
Key concepts: Variable (mathematics), Exponential function, Mathematics, Applied mathematics, Mathematical economics, Econometrics, Statistics, Mathematical analysis