On the equivalence of the sum and the maximal term of the Dirichlet series absolutely convergent in the half-plane
For absolutely convergent in the half-plane ${zcolon {mRe,}z<0}$ Dirichlet series $F(z)=sumlimits_{n=0}^{+infty}a_ne^{zlambda_n},$ where $0leqlambda_nuparrow +infty (0leq nuparrow+infty),$ we establish conditions on the coefficients of itsNewton majorant, sufficient for the relation $F(x+iy)=(1+o...
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Vasyl Stefanyk Precarpathian National University
2009-06-01
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| Series: | Karpatsʹkì Matematičnì Publìkacìï |
| Online Access: | http://journals.pu.if.ua/index.php/cmp/article/view/18/15 |
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doaj-717bbb36482e4f73947091306d408b992020-11-25T01:51:14ZengVasyl Stefanyk Precarpathian National UniversityKarpatsʹkì Matematičnì Publìkacìï2075-98272009-06-0111100106On the equivalence of the sum and the maximal term of the Dirichlet series absolutely convergent in the half-planeYa. Z. StasyukO. B. SkaskivFor absolutely convergent in the half-plane ${zcolon {mRe,}z<0}$ Dirichlet series $F(z)=sumlimits_{n=0}^{+infty}a_ne^{zlambda_n},$ where $0leqlambda_nuparrow +infty (0leq nuparrow+infty),$ we establish conditions on the coefficients of itsNewton majorant, sufficient for the relation $F(x+iy)=(1+o(1))a_{u(x)}e^{(x+iy)lambda_{u(x)}}$ to hold as$xo -0$ outside some set $E$ of zero logarithmic density in thepoint $0,$ uniformly by $yin{mathbb R}$.http://journals.pu.if.ua/index.php/cmp/article/view/18/15 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Ya. Z. Stasyuk O. B. Skaskiv |
| spellingShingle |
Ya. Z. Stasyuk O. B. Skaskiv On the equivalence of the sum and the maximal term of the Dirichlet series absolutely convergent in the half-plane Karpatsʹkì Matematičnì Publìkacìï |
| author_facet |
Ya. Z. Stasyuk O. B. Skaskiv |
| author_sort |
Ya. Z. Stasyuk |
| title |
On the equivalence of the sum and the maximal term of the Dirichlet series absolutely convergent in the half-plane |
| title_short |
On the equivalence of the sum and the maximal term of the Dirichlet series absolutely convergent in the half-plane |
| title_full |
On the equivalence of the sum and the maximal term of the Dirichlet series absolutely convergent in the half-plane |
| title_fullStr |
On the equivalence of the sum and the maximal term of the Dirichlet series absolutely convergent in the half-plane |
| title_full_unstemmed |
On the equivalence of the sum and the maximal term of the Dirichlet series absolutely convergent in the half-plane |
| title_sort |
on the equivalence of the sum and the maximal term of the dirichlet series absolutely convergent in the half-plane |
| publisher |
Vasyl Stefanyk Precarpathian National University |
| series |
Karpatsʹkì Matematičnì Publìkacìï |
| issn |
2075-9827 |
| publishDate |
2009-06-01 |
| description |
For absolutely convergent in the half-plane ${zcolon {mRe,}z<0}$ Dirichlet series $F(z)=sumlimits_{n=0}^{+infty}a_ne^{zlambda_n},$ where $0leqlambda_nuparrow +infty (0leq nuparrow+infty),$ we establish conditions on the coefficients of itsNewton majorant, sufficient for the relation $F(x+iy)=(1+o(1))a_{u(x)}e^{(x+iy)lambda_{u(x)}}$ to hold as$xo -0$ outside some set $E$ of zero logarithmic density in thepoint $0,$ uniformly by $yin{mathbb R}$. |
| url |
http://journals.pu.if.ua/index.php/cmp/article/view/18/15 |
| work_keys_str_mv |
AT yazstasyuk ontheequivalenceofthesumandthemaximaltermofthedirichletseriesabsolutelyconvergentinthehalfplane AT obskaskiv ontheequivalenceofthesumandthemaximaltermofthedirichletseriesabsolutelyconvergentinthehalfplane |
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1724997697985839104 |