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1.
For the Dirichlet series, we obtain a condition on the exponents for which the logarithms of the maximum of the modulus of its sum and of the maximal term are equivalent to the same convex function. 相似文献
2.
Let M() be the maximum modulus and let () be the maximum term of an entire Dirichlet series with nonnegative exponents
n
increasing to . We establish a condition for
n
under which the relations
and
are equivalent under certain conditions on the functions 1 and 2. 相似文献
3.
For entire Dirichlet series, we establish conditions on its coefficients and exponents under which the logarithms of the maximal term and of the maximum of the modulus are regularly varying functions of order [1, + ) and the central exponent is a regularly varying function of order – 1. 相似文献
4.
5.
Let (Ω,A,P) be a probability spasce. Consider a random Dirichlet series. 相似文献
6.
We establish a criterion for the logarithm of the maximal term of a Dirichlet series absolutely convergent in the half-plane to be equivalent on an asymptotic set to the logarithm of the maximal term of its Hadamard composition with any other Dirichlet series from a certain class. 相似文献
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8.
Dirichlet级数表示的整函数的增长性 总被引:14,自引:0,他引:14
本文系统地研究了在全平面上收敛的Dirichlet级数的增长性,得到了级数的系数和增长级之间关系的一系列充要条件. 相似文献
9.
邓冠铁 《数学物理学报(A辑)》2003,23(6):735-738
该文对一个由复指数Dirichlet 级数表示的,其系数满足一给定增长条件且在一固定水平带形有界不恒为零的整函数的存在性, 给出了充分必要条件。 相似文献
10.
该文研究了一般随机Dirichlet级数的所表示整函数增长性和值分布,得出了重要结论:在适当条件下,任何水平带形上或水平线上增长级与全面上相同,对于ρ随机Dirichlet级数(0<ρ<∞)a.s.在任何宽为〖SX(〗π[]ρ〖SX)〗的水平带形内,至少有一条ρ级没有有穷例外值的Borel线。 相似文献
11.
系统地研究了全平面收敛的B-值随机Difichlet级数的增长性,得到了在一定条件下,B-值随机Dirichlet级数在收敛平面上的增长(下)级几乎处处等于某Dirichlet级数的增长(下)级还得到了它们与指数和系数的关系式. 相似文献
12.
We establish a criterion for the logarithm of the maximal term of a Dirichlet series whose absolute convergence domain is a half-plane to be equivalent to the logarithm of the maximal term of its Hadamard composition with another Dirichlet series of some class on the asymptotic set. 相似文献
13.
For Dirichlet series with arbitrary abscissa of absolute convergence, we investigate the relationhip between the increase in the maximum term and
, q ∈ (0,+∞).__________Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 11, pp. 1501–1512, November, 2004. 相似文献
14.
由Dirichlet 级数表示的整函数f(z)在带形中有界,其系数{an}和指数 {λn}(n=1,2,... )是复数列.文中引入 φ-级 和下φ -级,讨论f(z) 具有φ -级和下φ -级的条件. 相似文献
15.
给出了超球级数所定义整函数的下阶、下型与极大项、中心指标、最大模之间的关系及几个不等式,并由此推出了超球级数成正规增长的充要条件及成完全正规增长的充要条件. 相似文献
16.
17.
We investigate Dirichlet series L(s, f) =
n=1
with q-periodic coefficients f(n), i.e. f(n+q) = f(n) for all integers n and some fixed integer q, and we prove an asymptotic formula for the number of nontrivial zeros of L(s, f). Further, we give a necessary condition for L(s, f) to have a distribution of the nontrivial zeros symmetrical with respect to the critical line. 相似文献
18.
Hardy and Wright (An Introduction to the Theory of Numbers, 5th edn., Oxford, 1979) recorded elegant closed forms for the generating functions of the divisor functions
k
(n) and
k
2(n) in the terms of Riemann Zeta function (s) only. In this paper, we explore other arithmetical functions enjoying this remarkable property. In Theorem 2.1 below, we are able to generalize the above result and prove that if f
i and g
i are completely multiplicative, then we have
where L
f(s) :=
n = 1
f(n)n
–s is the Dirichlet series corresponding to f. Let r
N(n) be the number of solutions of x
1
2 + ··· + x
N
2 = n and r
2,P
(n) be the number of solutions of x
2 + Py
2 = n. One of the applications of Theorem 2.1 is to obtain closed forms, in terms of (s) and Dirichlet L-functions, for the generating functions of r
N(n), r
N
2(n), r
2,P
(n) and r
2,P
(n)2 for certain N and P. We also use these generating functions to obtain asymptotic estimates of the average values for each function for which we obtain a Dirichlet series. 相似文献
19.
20.
关于两类狄里克莱级数系数的重排 总被引:1,自引:0,他引:1
研究了两类狄里克莱级数的系数重排后的增长性,得到了全平面和半平面上有限级狄里克莱级数的系数经过重排后级和型保持不变的充要条件. 相似文献