A logarithm type mean value theorem of the Riemann zeta function

doi:10.1016/j.jnt.2005.12.007

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	A logarithm type mean value theorem of the Riemann zeta function
	Ding, Xia-Qi; Feng, Shao-Ji
	2006-10-01
发表期刊	JOURNAL OF NUMBER THEORY
ISSN	0022-314X
卷号	120 期号:2 页码:206-212
摘要	For any integer K >= 2 and positive integer h, we investigate the mean value of vertical bar zeta(sigma + it)vertical bar(2k) x log(h) vertical bar zeta(sigma + it)vertical bar for all real number 0 < k < K and all sigma > 1 - 1/K. In case K = 2, h = 1, this has been studied by Wang in [F.T. Wang, A mean value theorem of the Riemann zeta function, Quart. J. Math. Oxford Ser. 18 (1947) 1-3]. In this note, we give a new brief proof of Wang's theorem, and, with this method, generalize it to the general case naturally. (c) 2006 Elsevier Inc. All rights reserved.
关键词	Riemann zeta function mean value theorem logarithm
DOI	10.1016/j.jnt.2005.12.007
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000240839400002
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/2660
专题	系统科学研究所
通讯作者	Feng, Shao-Ji
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Ding, Xia-Qi,Feng, Shao-Ji. A logarithm type mean value theorem of the Riemann zeta function[J]. JOURNAL OF NUMBER THEORY,2006,120(2):206-212.
APA	Ding, Xia-Qi,&Feng, Shao-Ji.(2006).A logarithm type mean value theorem of the Riemann zeta function.JOURNAL OF NUMBER THEORY,120(2),206-212.
MLA	Ding, Xia-Qi,et al."A logarithm type mean value theorem of the Riemann zeta function".JOURNAL OF NUMBER THEORY 120.2(2006):206-212.