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arXiv · 1010.0120

Estimates for exponential sums with a large automorphism group

Antonio Rojas-León
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Abstract

We prove some improvements of the classical Weil bound for one variable additive and multiplicative character sums associated to a polynomial over a finite field $k=\Fq$ for two classes of polynomials which are invariant under a large abelian group of automorphisms of the affine line $\AAA^1_k$: those invariant under translation by elements of $k$ and those invariant under homotheties with ratios in a large subgroup of the multiplicative group of $k$. In both cases, we are able to improve the bound by a factor of $\sqrt{q}$ over an extension of $k$ of cardinality sufficiently large compared to the degree of $f$.

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Antonio Rojas-León. 2010-10-01. Estimates for exponential sums with a large automorphism group. https://arxiv.org/abs/1010.0120

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