Kaluzhynova L. On the magnitudes of deviations of entire and meromorphic functions

The Eremenko’s deviations of entire functions from rational ones and of meromorphic functions from polynomials of degree not greater than are investigated. We obtained a sharp estimate for the sum of deviations of entire functions of finite lower order from rational functions. Also, an estimate for the sum of deviations of meromorphic functions from polynomials of degree not greater than by Valiron’s deficiency was obtained. We applied these results to the study of strong asymptotic values of entire and meromorphic functions. For functions meromorphic in the disk we investigated the magnitudes of deviations by Krytov.