Russian Mathematical Surveys
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Uspekhi Mat. Nauk:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Russian Mathematical Surveys, 1976, Volume 31, Issue 1, Pages 5–57
DOI: https://doi.org/10.1070/RM1976v031n01ABEH001444
(Mi rm3639)
 

This article is cited in 24 scientific papers (total in 25 papers)

Non-Archimedean integration and Jacquet–Langlands $p$-adic $L$-functions

Yu. I. Manin
References:
Abstract: In 1964 Kubota and Leopoldt constructed a $p$-adic analogue of the Riemann zeta-function. Since then the class of $L$-functions with $p$-adic variants has continually been enlarged. At the beginning of the article we survey work in this direction, using the technique of the $p$-adic Mellin transform. Then we show how to apply it to the construction of non-Archimedean measures and integrals corresponding to parabolic forms relative to the Hilbert groups. The exposition is in the adele language of Jacquet and Langlands. We construct $p$-adic $L$-functions associated with representations of $GL(2)$ over completely real fields, of discrete type at infinity.
Received: 30.07.1975
Bibliographic databases:
Document Type: Article
UDC: 517.5
MSC: 11M38, 11M26, 11M36
Language: English
Original paper language: Russian
Citation: Yu. I. Manin, “Non-Archimedean integration and Jacquet–Langlands $p$-adic $L$-functions”, Russian Math. Surveys, 31:1 (1976), 5–57
Citation in format AMSBIB
\Bibitem{Man76}
\by Yu.~I.~Manin
\paper Non-Archimedean integration and Jacquet--Langlands $p$-adic $L$-functions
\jour Russian Math. Surveys
\yr 1976
\vol 31
\issue 1
\pages 5--57
\mathnet{http://mi.mathnet.ru//eng/rm3639}
\crossref{https://doi.org/10.1070/RM1976v031n01ABEH001444}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=417134}
\zmath{https://zbmath.org/?q=an:0336.12007|0348.12016}
Linking options:
  • https://www.mathnet.ru/eng/rm3639
  • https://doi.org/10.1070/RM1976v031n01ABEH001444
  • https://www.mathnet.ru/eng/rm/v31/i1/p5
  • This publication is cited in the following 25 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Успехи математических наук Russian Mathematical Surveys
    Statistics & downloads:
    Abstract page:867
    Russian version PDF:368
    English version PDF:48
    References:67
    First page:3
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024