Separation of zeros of translates of polynomials and entire functions
For an entire function \(f\) with zeros (a), \(\delta(f)= \inf\{|a_i-a_j|: i\neq j\}\) is called the separation of zeros. In his earlier paper [Am. Math. Mon. 100, No. 3, 272-273 (1993; Zbl 0767.26010)] the author showed that \(\delta (f-kf) >\delta (f)\) for all \(k \mathbb{R}\), and in two later papers [J. Aust. Math. Soc., Ser. A 59, No. 2, 330-342 (1995; Zbl 0873.26006), Proc. Edinb. Math. Soc., II. Ser. 39, No. 3, 357-363 (1996; Zbl 0853.26009)] gave estimates of the increase of the separation of zeros. In the present paper the author gives the extensions of these results to entire functions of order less than 2.
scientific article; zbMATH DE number 1005583