RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






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


Mat. Sb., 2014, Volume 205, Number 10, Pages 107–124 (Mi msb8397)  

This article is cited in 1 scientific paper (total in 1 paper)

A holomorphic version of the Tate-Iwasawa method for unramified $L$-functions. I

A. N. Parshin

Steklov Mathematical Institute of Russian Academy of Sciences

Abstract: Using the Tate-Iwasawa method the problem of meromorphic continuation and of the existence of a functional equation can be solved for the zeta and $L$-functions of one-dimensional arithmetical schemes. A new version of this method is put forward, which looks at the case of curves over a finite field and of unramified $L$-functions. The proof is based on a reduction of the problem to a Cousin problem on the Riemann sphere which is related to the curve under consideration.
Bibliography: 16 titles.

Keywords: zeta function, analytic continuation, Poisson formula, sum of residues, Cousin problem.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00178-a
13-01-12420-офи-м2
Ministry of Education and Science of the Russian Federation НШ-2998.2014.1


DOI: https://doi.org/10.4213/sm8397

Full text: PDF file (584 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2014, 205:10, 1473–1491

Bibliographic databases:

Document Type: Article
UDC: 511.68+512.626
MSC: 11M41
Received: 25.06.2014

Citation: A. N. Parshin, “A holomorphic version of the Tate-Iwasawa method for unramified $L$-functions. I”, Mat. Sb., 205:10 (2014), 107–124; Sb. Math., 205:10 (2014), 1473–1491

Citation in format AMSBIB
\Bibitem{Par14}
\by A.~N.~Parshin
\paper A holomorphic version of the Tate-Iwasawa method for unramified $L$-functions.~I
\jour Mat. Sb.
\yr 2014
\vol 205
\issue 10
\pages 107--124
\mathnet{http://mi.mathnet.ru/msb8397}
\crossref{https://doi.org/10.4213/sm8397}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3289229}
\zmath{https://zbmath.org/?q=an:06406531}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2014SbMat.205.1473P}
\elib{http://elibrary.ru/item.asp?id=22834489}
\transl
\jour Sb. Math.
\yr 2014
\vol 205
\issue 10
\pages 1473--1491
\crossref{https://doi.org/10.1070/SM2014v205n10ABEH004426}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000346573300005}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84919683473}


Linking options:
  • http://mi.mathnet.ru/eng/msb8397
  • https://doi.org/10.4213/sm8397
  • http://mi.mathnet.ru/eng/msb/v205/i10/p107

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. D. V. Osipov, “Arithmetic surfaces and adelic quotient groups”, Izv. Math., 82:4 (2018), 817–836  mathnet  crossref  crossref  adsnasa  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
    Number of views:
    This page:349
    Full text:39
    References:31
    First page:23

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019