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摘要翻译：
本文介绍了与Laurent多项式F$相关的$T$-adic指数和。它们插值所有与$F$相关的经典$P^m$-次方阶指数和。建立了$T$-adic指数和的$L$-函数的牛顿多边形的Hodge界。这个界使我们能够对所有$M$确定与$F$有关的$P^m$-幂次指数和的$L$-函数的牛顿多边形，这对于$M=1$是普通的。本文还研究了$T$-adic指数和的$L$-函数的深层性质。在此过程中，讨论了关于$T$-adic指数和本身的新的开放问题。
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英文标题：
《T-adic exponential sums over finite fields》
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作者：
Chunlei Liu and Daqing Wan
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最新提交年份：
2009
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分类信息：
一级分类：Mathematics 数学
二级分类：Number Theory 数论
分类描述：Prime numbers, diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory
素数，丢番图方程，解析数论，代数数论，算术几何，伽罗瓦理论
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一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
$T$-adic exponential sums associated to a Laurent polynomial $f$ are introduced. They interpolate all classical $p^m$-power order exponential sums associated to $f$. The Hodge bound for the Newton polygon of $L$-functions of $T$-adic exponential sums is established. This bound enables us to determine, for all $m$, the Newton polygons of $L$-functions of $p^m$-power order exponential sums associated to an $f$ which is ordinary for $m=1$. Deeper properties of $L$-functions of $T$-adic exponential sums are also studied. Along the way, new open problems about the $T$-adic exponential sum itself are discussed.
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PDF链接：
https://arxiv.org/pdf/0802.2589
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