### Abstract

Let f (z) be a real entire function of genus 1*, Δ ≥ 0, and suppose that for each ε > 0, all but a finite number of the zeros of f(z) lie in the strip |Im z| ≤ ≤ Δ + ε. Let λ be a positive constant such that lim sup_{r → ∞} log M(r; f)/r^{2} < 1/(4λ). It is shown that for each ε > 0, all but a finite number of the zeros of the entire function e ^{-λD2} f(z) := ∑_{m=0}^{∞} (-λ)^{m}f^{(2m)}(z)/m! lie in the strip |Im z| ≤ √max{Δ^{2} - 2λ, 0} + ε; and if Δ ^{2} < 2λ, then all but a finite number of the zeros of e ^{-λD2} f(z) are real and simple. As a consequence, de Bruijn's question whether the functions e^{λt2}, λ > 0, are strong universal factors is answered affirmatively.

Original language | English |
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Pages (from-to) | 369-387 |

Number of pages | 19 |

Journal | Journal d'Analyse Mathematique |

Volume | 91 |

DOIs | |

Publication status | Published - 2003 Jan 1 |

### All Science Journal Classification (ASJC) codes

- Analysis
- Mathematics(all)

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## Cite this

*Journal d'Analyse Mathematique*,

*91*, 369-387. https://doi.org/10.1007/BF02788795