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Mathematics of the USSR-Izvestiya, 1972, Volume 6, Issue 1, Pages 19–64
DOI: https://doi.org/10.1070/IM1972v006n01ABEH001867
(Mi im2290)
 

This article is cited in 109 scientific papers (total in 110 papers)

Parabolic points and zeta-functions of modular curves

Yu. I. Manin
References:
Abstract: In this paper we obtain explicit formulas for the values at the center of the critical strip of Dirichlet series connected with weight 2 parabolic forms of the group $\Gamma_0(N)$. In particular, these formulas allow us to verify the Birch–Swinnerton-Dyer conjecture on the order of a zero for uniformizable elliptic curves over certain $\Gamma$-extensions. We also give applications to noncommutative reciprocity laws.
Received: 05.10.1971
Bibliographic databases:
Document Type: Article
UDC: 511
MSC: Primary 14G10; Secondary 14H99
Language: English
Original paper language: Russian
Citation: Yu. I. Manin, “Parabolic points and zeta-functions of modular curves”, Math. USSR-Izv., 6:1 (1972), 19–64
Citation in format AMSBIB
\Bibitem{Man72}
\by Yu.~I.~Manin
\paper Parabolic points and zeta-functions of modular curves
\jour Math. USSR-Izv.
\yr 1972
\vol 6
\issue 1
\pages 19--64
\mathnet{http://mi.mathnet.ru//eng/im2290}
\crossref{https://doi.org/10.1070/IM1972v006n01ABEH001867}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=314846}
\zmath{https://zbmath.org/?q=an:0243.14008}
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  • https://doi.org/10.1070/IM1972v006n01ABEH001867
  • https://www.mathnet.ru/eng/im/v36/i1/p19
  • This publication is cited in the following 110 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
     
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