Matematicheskie Zametki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Matematicheskie Zametki, 2021, Volume 110, Issue 4, Pages 524–536
DOI: https://doi.org/10.4213/mzm13163 (Mi mzm13163) 		 
On a Ramanujan Identity and Its Generalizations

A. T. Daniyarkhodzhaeva, M. A. Korolevb

a Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region
b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Full-text PDF (484 kB)
References:
PDF
HTML
DOI: https://doi.org/10.4213/mzm13163
Abstract: In the present paper, we propose a new method of derivation of number-theoretic identities which is applied to the proof of the multidimensional analogue of one of the Ramanujan identities. This method allows us to obtain new infinite series representations for the number $\pi$, of the values of the Riemann zeta function, and of the $L$-Dirichlet series at integer points.
Keywords: Ramanujan identity, hyperbolic functions, Dirichlet character modulo $4$.
Funding agency Grant number
Russian Science Foundation 19-11-00001
The research of the second author was carried out at the Steklov Mathematical Institute of Russian Academy of Sciences and was supported by the Grant of the Russian Science Foundation (project no. 19-11-00001).
Received: 27.05.2021
English version:
Mathematical Notes, 2021, Volume 110, Issue 4, Pages 511–521
DOI: https://doi.org/10.1134/S0001434621090212
Bibliographic databases:
Document Type: Article
UDC: 511.33
Language: Russian
Citation: A. T. Daniyarkhodzhaev, M. A. Korolev, “On a Ramanujan Identity and Its Generalizations”, Mat. Zametki, 110:4 (2021), 524–536; Math. Notes, 110:4 (2021), 511–521
Citation in format AMSBIB
\Bibitem{DanKor21}
\by A.~T.~Daniyarkhodzhaev, M.~A.~Korolev
\paper On a Ramanujan Identity and Its Generalizations
\jour Mat. Zametki
\yr 2021
\vol 110
\issue 4
\pages 524--536
\mathnet{http://mi.mathnet.ru/mzm13163}
\crossref{https://doi.org/10.4213/mzm13163}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4324030}
\elib{https://elibrary.ru/item.asp?id=47518058}
\transl
\jour Math. Notes
\yr 2021
\vol 110
\issue 4
\pages 511--521
\crossref{https://doi.org/10.1134/S0001434621090212}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000711049900021}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85118115249}
Linking options:
  • https://www.mathnet.ru/eng/mzm13163
  • https://doi.org/10.4213/mzm13163
  • https://www.mathnet.ru/eng/mzm/v110/i4/p524
    • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024