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Izv. RAN. Ser. Mat., 2008, Volume 72, Issue 3, Pages 19–68 (Mi izv1916)  

This article is cited in 4 scientific papers (total in 4 papers)

On the integral of Hardy's function $Z(t)$

M. A. Korolev

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We prove asymptotic formulae for the values of the integral of Hardy's function $Z(t)$ at special points and obtain an omega-theorem and an upper bound for the integral of $Z(t)$ that are sharp with respect to the rate of growth.

DOI: https://doi.org/10.4213/im1916

Full text: PDF file (724 kB)
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English version:
Izvestiya: Mathematics, 2008, 72:3, 429–478

Bibliographic databases:

UDC: 511
MSC: 11M06, 11M26
Received: 24.10.2006

Citation: M. A. Korolev, “On the integral of Hardy's function $Z(t)$”, Izv. RAN. Ser. Mat., 72:3 (2008), 19–68; Izv. Math., 72:3 (2008), 429–478

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Ivić A., “On some problems involving Hardy's function”, Centr. Eur. J. Math., 8:6 (2010), 1029–1040  crossref  mathscinet  zmath  isi  scopus
    2. Jutila M., “An asymptotic formula for the primitive of Hardy's function”, Ark. Mat., 49:1 (2011), 97–107  crossref  mathscinet  zmath  adsnasa  isi  scopus
    3. A. Ivić, “Hardy's function $Z(t)$: Results and problems”, Proc. Steklov Inst. Math., 296 (2017), 104–114  mathnet  crossref  crossref  mathscinet  isi  elib
    4. Matti Jutila, “An approximate functional equation for the primitive of Hardy's function”, Proc. Steklov Inst. Math., 299 (2017), 109–116  mathnet  crossref  crossref  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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