On the Distribution of Roots of Polynomials

  title={On the Distribution of Roots of Polynomials},
  author={Paul Erd{\"o}s and Paul Tur{\'a}n},
  journal={Annals of Mathematics},
1. We start by explaining two groups of theorems and we shall derive both from a common source. P. Bloch and G. P6lya' investigated first the question of giving an upper estimation of the number R of real roots of (1.1) f(z) = UIJ + Olc?T +. They proved that the number of real roots is* <-41G, $1 n log log n log n * A few years later Erhardt Schmidt3 proved the sharper inequality and the still sharper one RZ 6 A& /.~'>n log F (1.2) 
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