$p$-adic estimates for multiplicative character sums

Details $p$-adic estimates for multiplicative character sums $p$-adic estimates for multiplicative character sums

2011-03-29

arxiv.org/abs/1103.5513v1

Mathematics

Number Theory

9 pages

Scientific paper

This article is an expanded version of the talk given by the first author at the conference "Exponential sums over finite fields and applications" (ETH, Z\"urich, November, 2010). We state some conjectures on archimedian and $p$-adic estimates for multiplicative character sums over smooth projective varieties. We also review some of the results of J. Dollarhide, which formed the basis for these conjectures. Applying his results, we prove one of the conjectures when the smooth projective variety is ${\mathbb P}^n$ itself.

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