Zeros of sparse polynomials over local fields of characteristic p

Details Zeros of sparse polynomials over local fields of characteristic p Zeros of sparse polynomials over local fields of characteristic p

1998-06-12

arxiv.org/abs/math/9806070v1

Mathematics

Number Theory

6 pages, Latex 2e; to appear in Math. Res. Letters

Scientific paper

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.

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