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Mathematics of the USSR-Sbornik, 1974, Volume 24, Issue 3, Pages 345–371
DOI: https://doi.org/10.1070/SM1974v024n03ABEH001916
(Mi sm3758)
 

This article is cited in 12 scientific papers (total in 13 papers)

$p$-adic Hecke series of imaginary quadratic fields

M. M. Vishik, Yu. I. Manin
References:
Abstract: In this paper a $p$-adic analytic function of two variables is constructed whose values in some “common” domain coincide with the values of the family of Hecke $L$-series of an imaginary quadratic field. The functional equation for such a function is obtained. The $p$-adic Mellin integral transform is the main technique.
Bibliography: 13 titles.
Received: 22.04.1974
Bibliographic databases:
Document Type: Article
UDC: 511.4
MSC: Primary 10H10, 12B30; Secondary 10D15, 12B40, 44A15
Language: English
Original paper language: Russian
Citation: M. M. Vishik, Yu. I. Manin, “$p$-adic Hecke series of imaginary quadratic fields”, Math. USSR-Sb., 24:3 (1974), 345–371
Citation in format AMSBIB
\Bibitem{VisMan74}
\by M.~M.~Vishik, Yu.~I.~Manin
\paper $p$-adic Hecke series of imaginary quadratic fields
\jour Math. USSR-Sb.
\yr 1974
\vol 24
\issue 3
\pages 345--371
\mathnet{http://mi.mathnet.ru//eng/sm3758}
\crossref{https://doi.org/10.1070/SM1974v024n03ABEH001916}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=371861}
\zmath{https://zbmath.org/?q=an:0352.12013}
Linking options:
  • https://www.mathnet.ru/eng/sm3758
  • https://doi.org/10.1070/SM1974v024n03ABEH001916
  • https://www.mathnet.ru/eng/sm/v137/i3/p357
  • This publication is cited in the following 13 articles:
    1. Panchishkin A., “Families of Siegel Modular Forms, l-Functions and Modularity Lifting Conjectures”, Isr. J. Math., 185:1 (2011), 343–368  crossref  mathscinet  zmath  isi
    2. A. A. Panchishkin, “Two Modularity Lifting Conjectures for Families of Siegel Modular Forms”, Math. Notes, 88:4 (2010), 544–551  mathnet  crossref  crossref  mathscinet  isi
    3. A. A. Panchishkin, “Triple products of Coleman’s families”, Journal of Mathematical Sciences (New York), 149:3 (2008), 1246  crossref  mathscinet  zmath
    4. A. A. Panchishkin, “The Maass–Shimura differential operators and congruences between arithmetical Siegel modular forms”, Mosc. Math. J., 5:4 (2005), 883–918  mathnet  crossref  mathscinet  zmath
    5. Datskovsky B., Guerzhoy P., “Searching for Kummer Congruences in an Infinite Slope Family”, Math. Comput., 73:246 (2004), 861–868  crossref  mathscinet  zmath  isi
    6. A.A. Panchishkin, “Two variable p-adic L functions attached to eigenfamilies of positive slope”, Invent math, 154:3 (2003), 551  crossref  mathscinet  zmath  isi  elib
    7. V. G. Drinfeld, V. A. Iskovskikh, A. I. Kostrikin, A. N. Tyurin, I. R. Shafarevich, “Yurii Ivanovich Manin (on his 60th birthday)”, Russian Math. Surveys, 52:4 (1997), 863–873  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    8. Yoshitaka Maeda, “Generalized Bernoulli numbers and congruence of modular forms”, Duke Math. J., 57:2 (1988)  crossref
    9. Haberland K., “Periods of Modular-Forms of One Variable and Group Co-Homology .1.”, Math. Nachr., 112 (1983), 245–282  crossref  mathscinet  zmath  isi
    10. Cassounogues P., “P-Adic l-Functions for Elliptic-Curves with Complex Multiplication .1.”, Compos. Math., 42:1 (1980), 31–56  mathscinet  isi
    11. Yu. I. Manin, A. A. Panchishkin, “Convolutions of Hecke series and their values at lattice points”, Math. USSR-Sb., 33:4 (1977), 539–571  mathnet  crossref  mathscinet  zmath  isi
    12. Yu. I. Manin, “Non-Archimedean integration and Jacquet–Langlands $p$-adic $L$-functions”, Russian Math. Surveys, 31:1 (1976), 5–57  mathnet  crossref  mathscinet  zmath
    13. M. M. Vishik, “Non-Archimedean measures connected with Dirichlet series”, Math. USSR-Sb., 28:2 (1976), 216–228  mathnet  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    References:84
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