On the relationship between the maximal terms of two integral Dirichlet series and properties of the Taylor coefficients of integral functions
1 Department of Higher Mathematics named after Prof. Mozhara V.I., Kyiv National University of Food Technologies, Kyiv, 01033, Ukraine
2 Department of theory of functions and functional analysis, Ivan Franko National University of Lviv, Lviv, 79007, Ukraine
Keywords:
Dirichlet series, Taylor coefficients
Abstract
A relation between the growth of the maximal terms of two entire Dirichlet series is established.
The obtained result is applied to the generalisation of Renyi theorems on the lacunarity of power
development of entire function.
References
Fabry E. Sur les series de Taylor qui out une infinite de points singularies // Acta Math. - 1899. T. 22. - P. 65-77.
Renyi C. On a conjecture of G. Polya // Acta Math. Acad. Sci. Hung. - 1956. - T. 7, N 2. - P. 145149.
Renyi A., Renyi C. On "small"coefficients of the power series of entire functions // Ann. Univ. Sci. Budapest. de Rolando E¨otvo¨snominantae, Sec. Math. - 1963. - T. 6. - P. 27-38.
Леонтьев А.Ф. Ряды экспонент. - М.: Наука, 1976. - 536 с.
Sheremeta M.M. On two classes of positive functions and belonging to them of main characteristics of entire functions // Mat. Stud. - 2003. - V. 19, N 1. - P. 73-82.
Cite
- ACS Style
- Mulyava, O.M.; Sheremeta, M. On the relationship between the maximal terms of two integral Dirichlet series and properties of the Taylor coefficients of integral functions. Bukovinian Mathematical Journal. 2018, 5
- AMA Style
- Mulyava OM, Sheremeta M. On the relationship between the maximal terms of two integral Dirichlet series and properties of the Taylor coefficients of integral functions. Bukovinian Mathematical Journal. 2018; 5(3-4).
- Chicago/Turabian Style
- Oksana Myroslavivna Mulyava, Myroslav Sheremeta. 2018. "On the relationship between the maximal terms of two integral Dirichlet series and properties of the Taylor coefficients of integral functions". Bukovinian Mathematical Journal. 5 no. 3-4.
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