Abstract
We relate the size of the factors of a polynomial with the repartition of its zeroz. First, we show that a polynomial with zeros on the unit circle always has a factor which is exponentially large. Then we give a symbolic formula, valid in the distribution sense, which allows one to reconstruct a polynomial from the repartition function of its zeros. From this formula we deduce a reciprocal to a well-known result of Erdos and Turan. We deal here with polynomials with complex coefficients, normalized with leading coefficient 1. We write such a polynomial under the form
Keywords:
*Supported in part by Contract 89/1377, Ministry of Defecse, D.G.A./D.R.E.T.-France
*Supported in part by Contract 89/1377, Ministry of Defecse, D.G.A./D.R.E.T.-France
Notes
*Supported in part by Contract 89/1377, Ministry of Defecse, D.G.A./D.R.E.T.-France