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Publication - Dr Edward Crane

    A bound for Smale's mean value conjecture for complex polynomials

    Citation

    Crane, E, 2007, ‘A bound for Smale's mean value conjecture for complex polynomials’. Bulletin of the London Mathematical Society, vol 39 (5)., pp. 781 - 791

    Abstract

    Smale's mean value conjecture is an inequality that relates the locations of critcal points and critical avalues of a polynomial p to the value and derivative of p at some given non-critical point. Using known estimatates for the logarithmic capacity of a connected set in the plane containing three given points, we give a new bound for the constant in Smale's inequality in terms of the degree d of p. The bound improves previous results when d > 8.

    Full details in the University publications repository