Iterating the Minimum Modulus: Functions of Order Half, Minimal Type

نویسندگان

چکیده

Abstract For a transcendental entire function f , the property that there exists $$r>0$$ r > 0 such $$m^n(r)\rightarrow \infty $$ m n ( ) → ∞ as $$n\rightarrow where $$m(r)=\min \{|f(z)|:|z|=r\}$$ = min { | f z : } is related to conjectures of Eremenko and Baker, for both which order 1/2 minimal type significant rate growth. We show this holds functions if maximum modulus has sufficiently regular growth we give examples sharpness our results by using recent generalisation Kjellberg’s method constructing small growth, allows rather precise control m ( r ).

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ژورنال

عنوان ژورنال: Computational Methods and Function Theory

سال: 2021

ISSN: ['2195-3724', '1617-9447']

DOI: https://doi.org/10.1007/s40315-021-00400-w