Zeros of sparse polynomials over local fields of characteristic p
Abstract
Let K be Fq((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 qk 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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