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April, 2005 On a mean value formula for the approximate functional equation of $\bm{\zeta(s)}$ in the critical strip
Shao-Ji FENG
J. Math. Soc. Japan 57(2): 513-521 (April, 2005). DOI: 10.2969/jmsj/1158242068

Abstract

In a recent paper, Isao Kiuchi and Naoki Yanagisawa studied the even power moments of the error term in the approximate functional equation for ζ ( s ) . They got a mean value formula with an error term O ( T 1 / 2 - k σ ) , and then they conjecture that this term could be replaced by E k , σ T 1 / 2 - k σ ( 1 + o ( 1 ) ) with constant E k , σ depending on k and σ . In this paper, we disprove this conjecture by showing that the error term should be f ( T ) T 1 / 2 - k σ + o ( T 1 / 2 - k σ ) with f ( T ) oscillating.

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Shao-Ji FENG. "On a mean value formula for the approximate functional equation of $\bm{\zeta(s)}$ in the critical strip." J. Math. Soc. Japan 57 (2) 513 - 521, April, 2005. https://doi.org/10.2969/jmsj/1158242068

Information

Published: April, 2005
First available in Project Euclid: 14 September 2006

zbMATH: 1176.11040
MathSciNet: MR2123242
Digital Object Identifier: 10.2969/jmsj/1158242068

Subjects:
Primary: 11M06

Keywords: approximate functional equation , mean value , Riemann zeta function

Rights: Copyright © 2005 Mathematical Society of Japan

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Vol.57 • No. 2 • April, 2005
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