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For a given collection of distinct arguments ~ =( 1 ;::: ; t), multiplicities ~ k =( k 1 ;::: ; k t ) ; and a real interval I =( U; V ) containing zero, we are interested in determining the smallest r for which there is a power series f(x )=1 + P 1 n=1 anx n with coecients an in I ,a nd roots 1 =re2i

Double roots of [-1,1] power series and related matters