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arxiv: 0901.0354 · v6 · submitted 2009-01-04 · 🧮 math.NT · math.AG

Generic T-adic exponential sums in one variable

classification 🧮 math.NT math.AG
keywords exponentialgenericpolygonnewtonsumst-adicvariableadic
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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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