On a mean value formula for the approximate functional equation of zeta(s) in the critical strip

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	On a mean value formula for the approximate functional equation of zeta(s) in the critical strip
	Feng, SJ
	2005-04-01
发表期刊	JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN
ISSN	0025-5645
卷号	57 期号:2 页码:513-521
摘要	In a recent paper, Isao Kiuchi and Naoki Yanagisawa studied the even power moments of the error term in the approximate functional equation for zeta(s). They got a mean value formula with an error term O(T1/2-k sigma), and then they conjecture that this term could be replaced by E-k,E-sigma T1/2-k sigma (1 + o(1)) with constant E-k,E-sigma depending on k and sigma. In this paper, we disprove this conjecture by showing that the error term should be f(T)T1/2-k sigma + o(T1/2-k sigma) with f (T) oscillating.
关键词	Riemann zeta function approximate functional equation mean value
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000228886000008
出版者	MATH SOC JAPAN
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/1854
专题	系统科学研究所
通讯作者	Feng, SJ
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	Feng, SJ. On a mean value formula for the approximate functional equation of zeta(s) in the critical strip[J]. JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN,2005,57(2):513-521.
APA	Feng, SJ.(2005).On a mean value formula for the approximate functional equation of zeta(s) in the critical strip.JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN,57(2),513-521.
MLA	Feng, SJ."On a mean value formula for the approximate functional equation of zeta(s) in the critical strip".JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN 57.2(2005):513-521.