On the ‘pits effect’ of Littlewood and Offord
| Autor: | Alexandre Eremenko, Iossif Ostrovskii |
|---|---|
| Rok vydání: | 2007 |
| Předmět: |
Mathematics - Complex Variables
General Mathematics Entire function 010102 general mathematics Mathematical analysis 0102 computer and information sciences Function (mathematics) 01 natural sciences Combinatorics 30B10 30D10 30D15 010201 computation theory & mathematics FOS: Mathematics Order (group theory) Complex Variables (math.CV) 0101 mathematics Constant (mathematics) Mathematics |
| Zdroj: | Bulletin of the London Mathematical Society |
| ISSN: | 0024-6093 |
| Popis: | Suppose that the moduli of the coefficients of a power series are 1/n!, while the arguments are arbitrary. If an entire function f represented by such power series decreases exponentially on some ray, then it has to be an exponential. If the arguments of the coefficients are of the form 2pi n^2a, where a is irrational, then the function displays the so-called "pits effect". More precisely, under this condition, f is of completely regular growth with constant indicator. Comment: 17 pages |
| Databáze: | OpenAIRE |
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