On zeros of functions of given proximate formal order analytic in a half-plane

  • B. V. Vynnyts’kyi
  • V.L. Sharan


We describe sequences of zeros of functionsf≢0 that are analytic in the half-plane ℂ+={z:Rez> and satisfy the condition $$\forall \varepsilon > 0\exists c_1 \in (0; + \infty )\forall z \in \mathbb{C}_{\text{ + }} :\left| {f(z)} \right| \leqslant c_1 \exp \left( {(\sigma + \varepsilon )\left| z \right|\eta (\left| z \right|)} \right)$$ where 0≤σ<+∞ and η is a positive function continuously differentiable on [0; +∞) and such thatxη′(x)/η(x)→0 asx→+∞.
How to Cite
Vynnyts’kyi, B. V., and V. Sharan. “On Zeros of Functions of Given Proximate Formal Order Analytic in a Half-Plane”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 51, no. 7, July 1999, pp. 904–909, https://umj.imath.kiev.ua/index.php/umj/article/view/4679.
Research articles