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Izv. Akad. Nauk SSSR Ser. Mat., 1980, Volume 44, Issue 3, Pages 670–718 (Mi izv1744)  

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

Shimura integrals of cusp forms

V. V. Shokurov


Abstract: This paper studies integrals of the form $\int_\alpha^{i\infty}\Phi z^k dz$ on the upper half-plane, where $\alpha$ is a rational number, $0\leqslant k\leqslant w$ is integral, and $\Phi$ is a cusp form of weight $w+2$ with respect to some modular group $\Gamma\subset\mathrm{SL}(2,\mathbf Z)$. The main result is that if $\Gamma$ is a congruence subgroup and $\Phi$ is an eigenvector of all the Hecke operators, then all these integrals are representable as linear combinations of two complex numbers with coefficients in some field of algebraic numbers.
Bibliography: 13 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1981, 16:3, 603–646

Bibliographic databases:

UDC: 517.4
MSC: Primary 10D15; Secondary 14E15
Received: 11.10.1979

Citation: V. V. Shokurov, “Shimura integrals of cusp forms”, Izv. Akad. Nauk SSSR Ser. Mat., 44:3 (1980), 670–718; Math. USSR-Izv., 16:3 (1981), 603–646

Citation in format AMSBIB
\Bibitem{Sho80}
\by V.~V.~Shokurov
\paper Shimura integrals of cusp forms
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1980
\vol 44
\issue 3
\pages 670--718
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=582162}
\zmath{https://zbmath.org/?q=an:0466.14014|0444.14030}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1981IzMat..16..603S}
\transl
\jour Math. USSR-Izv.
\yr 1981
\vol 16
\issue 3
\pages 603--646
\crossref{https://doi.org/10.1070/IM1981v016n03ABEH001322}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1981MK41200006}


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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. Min Ho Lee, “On the Kronecker pairing for mixed cusp forms”, manuscripta math, 71:1 (1991), 35  crossref  mathscinet  zmath  isi
    2. Min Ho Lee, “Periods of mixed cusp forms”, manuscripta math, 73:1 (1991), 163  crossref  mathscinet  zmath  isi
    3. Yu. I. Manin, “Iterated Shimura integrals”, Mosc. Math. J., 5:4 (2005), 869–881  mathnet  mathscinet  zmath
    4. François Martin, “Périodes de formes modulaires de poids 1”, Journal of Number Theory, 116:2 (2006), 399  crossref
    5. YoungJu Choie, Kentaro Ihara, “Iterated period integrals and multiple Hecke L-functions”, manuscripta math, 2013  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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