Zeros of sparse polynomials over local fields of characteristic p
Number Theory
2017-04-03 v1 Commutative Algebra
Abstract
Let K be F_q((T)), or more generally any field of characteristic p equipped with a valuation having a finite residue field of q elements. Then a polynomial f(x) in K[x] having k+1 nonzero coefficients has at most q^k distinct zeros in K. We also obtain the best possible bound for the number of zeros of degree at most d over K.
Cite
@article{arxiv.math/9806070,
title = {Zeros of sparse polynomials over local fields of characteristic p},
author = {Bjorn Poonen},
journal= {arXiv preprint arXiv:math/9806070},
year = {2017}
}
Comments
6 pages, Latex 2e; to appear in Math. Res. Letters