The argument of the Riemann zeta function (Q2862881)

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scientific article; zbMATH DE number 6228967
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The argument of the Riemann zeta function
scientific article; zbMATH DE number 6228967

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    19 November 2013
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    Riemann zeta function
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    argument of the zeta function
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    short intervals
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    The argument of the Riemann zeta function (English)
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    The author gives a survey of results on the argument of the Riemann zeta function \(\zeta(s)\), \(s=\sigma+it\), obtained by \textit{A. A. Karatsuba} and \textit{M. A. Korolev} [Russ. Math. Surv. 61, No. 3, 389--482 (2006); translation from Usp. Mat. Nauk 61, No. 3, 3--92 (2006; Zbl 1215.11081)], \textit{R. C. Vaughan} and \textit{T. D. Wooley} [Bull. Lond. Math. Soc. 30, No. 2, 113--122 (1998; Zbl 0934.11037)], \textit{M. A. Korolev} [Dokl. Math. 78, No. 1, 531--534 (2008); translation from Dokl. Akad. Nauk., Ross. Akad. Nauk. 421, No. 3, 308--311 (2008; Zbl 1221.11182); Izv. Math. 69, No. 4, 719--731 (2005); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 69, No. 4, 75--88 (2005; Zbl 1084.11051); Izv. Math. 70, No. 3, 427--446 (2006); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 70, No. 3, 3--22 (2006; Zbl 1187.11027)]. He shows that the sign change, the large values of the argument of the function \(\zeta(s)\) on short intervals, and so on are consequences of more general statements obtained by the author in 2009. Note that, in the list of references, there are no quotations to the works of author in period 2009--2010 or early works with exception [\textit{R. N. Boyarinov} and \textit{V. N. Chubarikov}, Dokl. Math. 64, No. 1, 3--5 (2001); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 379, No. 1, 9--11 (2001; Zbl 1090.11502)].
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