ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 30D15, 30D20 Prytula, Yaroslav Ya., Lviv State University, Ukraine Generalization of Lindelöf Theorem Necessary and sufficient conditions are established on the coefficients of an entire Dirichlet series that defines a function F for fulfilling the correlation ln M(σ, F) = Φ(σ + o(1)), whenever σ → ∞, where M(σ, F) = sup{|F (σ + it)| : t ∈ ℝ}, and Φ is a positive on (−∞, +∞) function such that 0 ≤ Φ′(x) ↑ +∞ (−∞ < x → +∞). If Φ(σ) = τ exp{ϱσ}, τ, ϱ ∈ (0, +∞) then the classic Lindelöf Theorem follows from the above correlation. References: 1. E. Lindelöf, Sur la determination de la croissance des fonctions entiere definies par un developpement de Taylor, Bull. Soc. Math. 27(1) (1903), 1–62.

2. Ya. Ya. Prytula, On the Lindelöf Theorem, Mat. Studii 8(1) (1997), 31–42.