2013•International Mathematics Research NoticesRequires access
A Sum–Product Theorem in Function Fields
Thomas F. Bloom, Timothy G. F. Jones
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Abstract
Let A be a finite subset of , the field of Laurent series in 1/t over a finite field . We show that, for any ϵ>0, there exists a constant C dependent only on ϵ and q such that . In particular, such a result is obtained for the rational function field . Identical results are also obtained for finite subsets of the p-adic field for any prime p.