## Abstract

Let f and f^{~} be entire functions of order less than two, and Ω = {z ∈ C: |z| = 1}. Let i_{in}(f) and i_{out}(f) denote the numbers of the zeros of f taken with their multiplicities located inside and outside Ω, respectively. Besides, i_{out}(f) can be infinite. We consider the following problem: how “close” should f and f^{~} be in order to provide the equalities i_{in}(f^{~}) = i_{in}(f) and i_{out}(f^{~}) = i_{out}(f)? If for f we have the lower bound on the boundary, that problem sometimes can be solved by the Rouché theorem, but the calculation of such a bound is often a hard task. We do not require the lower bounds. We restrict ourselves by functions of order no more than two. Our results are new even for polynomials.

Original language | English |
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Pages (from-to) | 583-588 |

Number of pages | 6 |

Journal | Rocky Mountain Journal of Mathematics |

Volume | 50 |

Issue number | 2 |

DOIs | |

State | Published - 1 Apr 2020 |

## Keywords

- Entire functions
- Perturbations
- Zeros

## ASJC Scopus subject areas

- General Mathematics