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Mosc. Math. J., 2005, Volume 5, Number 4, Pages 869–881 (Mi mmj226)  

This article is cited in 10 scientific papers (total in 10 papers)

Iterated Shimura integrals

Yu. I. Manin

Max Planck Institute for Mathematics

Abstract: In this paper, I continue the study of iterated integrals of modular forms and noncommutative modular symbols for $\Gamma\subsetSL(2,\mathbb Z)$ started in my paper math.NT/0502576. The main new results involve a description of the iterated Shimura cohomology and the image of the iterated Shimura cocycle class inside it. The concluding section of the paper contains a concise review of the classical modular symbols for $SL(2)$ and a discussion of open problems.

Key words and phrases: Iterated integrals, modular forms, modular symbols, multiple zeta values.

DOI: https://doi.org/10.17323/1609-4514-2005-5-4-869-881

Full text: http://www.ams.org/.../abst5-4-2005.html
References: PDF file   HTML file

Bibliographic databases:

MSC: Primary 11F67, 11M41; Secondary 11G55
Received: September 7, 2005
Language:

Citation: Yu. I. Manin, “Iterated Shimura integrals”, Mosc. Math. J., 5:4 (2005), 869–881

Citation in format AMSBIB
\Bibitem{Man05}
\by Yu.~I.~Manin
\paper Iterated Shimura integrals
\jour Mosc. Math.~J.
\yr 2005
\vol 5
\issue 4
\pages 869--881
\mathnet{http://mi.mathnet.ru/mmj226}
\crossref{https://doi.org/10.17323/1609-4514-2005-5-4-869-881}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2266463}
\zmath{https://zbmath.org/?q=an:05182616}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000208595600009}


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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. Petersen D., “Cusp Form Motives and Admissible G-Covers”, Algebr. Number Theory, 6:6 (2012), 1199–1221  crossref  mathscinet  zmath  isi  scopus
    2. Choie Y., Ihara K., “Iterated Period Integrals and Multiple Hecke l-Functions”, Manuscr. Math., 142:1-2 (2013), 245–255  crossref  mathscinet  zmath  isi  scopus
    3. Manin Yu.I., “Non-Commutative Generalized Dedekind Symbols”, Pure Appl. Math. Q., 10:2, SI (2014), 245–258  crossref  mathscinet  zmath  isi  scopus
    4. Choie Y., Matsumoto K., “Functional Equations For Double Series of Euler Type With Coefficients”, Adv. Math., 292 (2016), 529–557  crossref  mathscinet  zmath  isi  scopus
    5. Choie Y., “Parabolic Cohomology and Multiple Hecke l-Values”, Ramanujan J., 41:1-3 (2016), 543–561  crossref  mathscinet  zmath  isi  scopus
    6. Bruggeman R.W., Choie Y., “Multiple Period Integrals and Cohomology”, Algebr. Number Theory, 10:3 (2016), 645–664  crossref  mathscinet  zmath  isi  scopus
    7. Brown F., “Zeta Elements in Depth 3 and the Fundamental Lie Algebra of the Infinitesimal Tate Curve”, Forum Math. Sigma, 5 (2017), e1  crossref  mathscinet  zmath  isi
    8. Brown F., “A Class of Non-Holomorphic Modular Forms i”, Res. Math. Sci., 5 (2018), 7  crossref  mathscinet  isi  scopus
    9. Manin Yu.I., “Modular Forms of Real Weights and Generalised Dedekind Symbols”, Res. Math. Sci., 5 (2018), 2  crossref  mathscinet  isi  scopus
    10. Cherednik I., “Riemann Hypothesis For Daha Superpolynomials and Plane Curve Singularities”, Commun. Number Theory Phys., 12:3 (2018), 409–490  crossref  mathscinet  zmath  isi  scopus
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