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Izv. RAN. Ser. Mat., 2001, Volume 65, Issue 1, Pages 93–106 (Mi izv322)  

This article is cited in 5 scientific papers (total in 5 papers)

An asymptotic formula for the Taylor coefficients of the function $\xi(s)$

L. D. Pustyl'nikov

M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences

Abstract: An asymptotic formula is derived for the Taylor coefficients of the function
$$ \xi(s)=\frac12s(s-1)\pi^{-s/2}\Gamma(\frac s2)\zeta(s) $$
at the point $s=1/2$.

DOI: https://doi.org/10.4213/im322

Full text: PDF file (638 kB)
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English version:
Izvestiya: Mathematics, 2001, 65:1, 85–98

Bibliographic databases:

MSC: 11M06, 11M26, 11M35, 11N05, 11M41
Received: 23.12.1999

Citation: L. D. Pustyl'nikov, “An asymptotic formula for the Taylor coefficients of the function $\xi(s)$”, Izv. RAN. Ser. Mat., 65:1 (2001), 93–106; Izv. Math., 65:1 (2001), 85–98

Citation in format AMSBIB
\Bibitem{Pus01}
\by L.~D.~Pustyl'nikov
\paper An asymptotic formula for the Taylor coefficients of the function~$\xi(s)$
\jour Izv. RAN. Ser. Mat.
\yr 2001
\vol 65
\issue 1
\pages 93--106
\mathnet{http://mi.mathnet.ru/izv322}
\crossref{https://doi.org/10.4213/im322}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1829406}
\zmath{https://zbmath.org/?q=an:1019.11023}
\transl
\jour Izv. Math.
\yr 2001
\vol 65
\issue 1
\pages 85--98
\crossref{https://doi.org/10.1070/im2001v065n01ABEH000322}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33747110600}


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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. L. D. Pustyl'nikov, “Refutation of an analogue of the Riemann hypothesis about zeros for an arbitrarily sharp approximation of the zeta-function satisfying the same functional equation”, Russian Math. Surveys, 58:1 (2003), 193–194  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. L. D. Pustylnikov, T. V. Lokot, “Novye rezultaty ob $L$-funktsiyakh Dirikhle”, Preprinty IPM im. M. V. Keldysha, 2008, 069, 10 pp.  mathnet
    3. L. D. Pustylnikov, “O gipoteze Rimana dlya priblizhënnoi dzeta-funktsii”, Preprinty IPM im. M. V. Keldysha, 2008, 070, 6 pp.  mathnet
    4. L. D. Pustylnikov, “O klassicheskoi dzeta-funktsii Rimana”, Preprinty IPM im. M. V. Keldysha, 2012, 027, 17 pp.  mathnet
    5. Griffin M., Ono K., Rolen L., Zagier D., “Jensen Polynomials For the Riemann Zeta Function and Other Sequences”, Proc. Natl. Acad. Sci. U. S. A., 116:23 (2019), 11103–11110  crossref  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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