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Published online by Cambridge University Press: 01 November 1999
We construct univalent functions in the unit disc, whose coefficient sequences (an) have arbitrarily long intervals of zeros and at the same time arbitrarily long intervals where [mid ]an[mid ] > nεn holds, (εn) being an arbitrary prescribed sequence of positive numbers tending to zero. Furthermore we show that the initial interval of coefficients of such a function can be prescribed to be any interior point of the coefficient region.