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Mosc. Math. J., 2002, Volume 2, Number 2, Pages 313–328 (Mi mmj57)  

This article is cited in 11 scientific papers (total in 11 papers)

A new method of constructing $p$-adic $L$-functions associated with modular forms

A. A. Panchishkin

University of Grenoble 1 — Joseph Fourier

Abstract: We give a new method of constructing admissible $p$-adic measures associated with modular cusp eigenforms, starting from distributions with values in spaces of modular forms. A canonical projection operator is used onto the characteristic subspace of an eigenvalue $\alpha$ of the Atkin–Lehner operator $U_p$. An algebraic version of nearly holomorphic modular forms is given and used in constructing $p$-adic measures.

Key words and phrases: Modular forms, Eisenstein series, $p$-adic $L$-functions, special values.

DOI: https://doi.org/10.17323/1609-4514-2002-2-2-313-328

Full text: http://www.ams.org/.../abst2-2-2002.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 11F33, 11F67, 11F30
Received: December 3, 2001; in revised form February 28, 2002
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Citation: A. A. Panchishkin, “A new method of constructing $p$-adic $L$-functions associated with modular forms”, Mosc. Math. J., 2:2 (2002), 313–328

Citation in format AMSBIB
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\paper A~new method of constructing $p$-adic $L$-functions associated with modular forms
\jour Mosc. Math.~J.
\yr 2002
\vol 2
\issue 2
\pages 313--328
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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. Courtieu M., Panchishkin A., Non-Archimedean $L$-functions and arithmetical Siegel modular forms, Lecture Notes in Math., 1471, Second edition, Springer-Verlag, Berlin, 2004, viii+196 pp.  crossref  mathscinet  zmath  isi
    2. Colmez P., “La conjecture de Birch et Swinnerton-Dyer $p$-adique [The $p$-adic Birch–Swinnerton-Dyer conjecture]”, Astérisque, 294, 2004, 251–319  mathscinet  zmath  isi
    3. A. A. Panchishkin, “The Maass–Shimura differential operators and congruences between arithmetical Siegel modular forms”, Mosc. Math. J., 5:4 (2005), 883–918  mathnet  mathscinet  zmath
    4. A. A. Panchishkin, “Triple products of Coleman's families”, J. Math. Sci., 149:3 (2008), 1246–1254  mathnet  crossref  mathscinet  zmath  elib
    5. Panchishkin A.A., “$p$-adic Banach modules of arithmetical modular forms and triple products of Coleman's families”, Pure Appl. Math. Q., 4:4 (2008), 1133–1164  crossref  mathscinet  zmath  isi
    6. Boecherer S., Panchishkin A.A., “p-adic Interpolation for Triple L-functions: Analytic Aspects”, Automorphic Forms and l-Functions II. Local Aspects, Contemporary Mathematics, 489, 2009, 1–39  crossref  mathscinet  zmath  isi
    7. Vienney M., “A New Construction of $p$-Adic Rankin Convolutions in the Case of Positive Slope”, Int J Number Theory, 6:8 (2010), 1875–1900  crossref  mathscinet  zmath  isi
    8. A. A. Panchishkin, “On zeta functions and families of Siegel modular forms”, J. Math. Sci., 180:5 (2012), 626–640  mathnet  crossref  mathscinet  elib
    9. Panchishkin A., “Families of Siegel modular forms, L-functions and modularity lifting conjectures”, Israel J Math, 185:1 (2011), 343–368  crossref  mathscinet  zmath  isi
    10. Panchishkin A., “Analytic Constructions of P-Adic l-Functions and Eisenstein Series”, Automorphic Forms and Related Geometry: Assessing the Legacy of i.i. Piatetski-Shapiro, Contemporary Mathematics, 614, eds. Cogdell J., Shahidi F., Soudry D., Amer Mathematical Soc, 2014, 345–374  crossref  mathscinet  zmath  isi
    11. Wang Sh., “the System of Euler of Kato in Family (i)”, Comment. Math. Helv., 89:4 (2014), 819–865  crossref  mathscinet  zmath  isi
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