Sequences of maximal terms and central exponents of derivatives of Dirichlet series期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

首页 | 本学科首页

官方微博 | 高级检索

按检索

Sequences of maximal terms and central exponents of derivatives of Dirichlet series

Authors:

M N Sheremeta

Institution:

(1) Lvov State University, USSR

Abstract:

For the Dirichlet series corresponding to a functionF with positive exponents increasing to ∞ and with abscissa of absolute convergenceA ∈ (−∞, +∞], it is proved that the sequences (μ(σ, F ^(m))) of maximal terms and (Λ(σ, F ^(m))) of central exponents are nondecreasing to ∞ asm → ∞ for any givenσ <A, and

$\overline {\mathop {\lim }\limits_{m \to \infty } } \frac{{\ln \mu (\sigma ,F^{(m)} )}}{{m\ln m}} \leqslant 1 and \mathop {\overline {\lim } }\limits_{m \to \infty } \frac{{\ln \Lambda (\sigma ,F^{(m)} )}}{{\ln m}} \leqslant 1.$

Necessary and sufficient conditions for putting the equality sign and replacing lim by lim in these relations are given. Translated fromMatematicheskie Zametki, Vol. 63, No. 3, pp. 457–467, March, 1998.

Keywords:

Dirichlet series maximal term central exponent

本文献已被 SpringerLink 等数据库收录！

设为首页 | 免责声明 | 关于勤云 | 加入收藏