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April 2011 An asymptotic formula for the primitive of Hardy’s function
Matti Jutila
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Ark. Mat. 49(1): 97-107 (April 2011). DOI: 10.1007/s11512-010-0122-4

Abstract

Let Z(t) be the classical Hardy function in the theory of Riemann’s zeta-function. An asymptotic formula with an error term O(T1/6log T) is given for the integral of Z(t) over the interval [0, T], with special attention paid to the critical cases when the fractional part of $\sqrt{T/2\pi }$ is close to $\frac{1}{4}$ or $\frac{3}{4}$.

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Matti Jutila. "An asymptotic formula for the primitive of Hardy’s function." Ark. Mat. 49 (1) 97 - 107, April 2011. https://doi.org/10.1007/s11512-010-0122-4

Information

Received: 19 March 2009; Revised: 3 February 2010; Published: April 2011
First available in Project Euclid: 31 January 2017

zbMATH: 1241.11100
MathSciNet: MR2784259
Digital Object Identifier: 10.1007/s11512-010-0122-4

Rights: 2010 © Institut Mittag-Leffler

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Vol.49 • No. 1 • April 2011
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