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arXiv · 1709.01663

Stratification for multiplicative character sums

Junyan Xu
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Abstract

We prove a stratification result for certain families of $n$-dimensional (complete algebraic) multiplicative character sums. The character sums we consider are sums of products of $r$ multiplicative characters evaluated at rational functions, and the families (with $nr$ parameters) are obtained by allowing each of the $r$ rational functions to be replaced by an "offset", i.e. a translate, of itself. For very general such families, we show that the stratum of the parameter space on which the character sum has maximum weight $n+j$ has codimension at least $j\lfloor(r-1)/2(n-1)\rfloor$ for $1\le j\le n-1$ and $\lceil nr/2\rceil$ for $j=n$.

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Junyan Xu. 2017-09-06. Stratification for multiplicative character sums. https://arxiv.org/abs/1709.01663

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