RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
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



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






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


Izv. RAN. Ser. Mat., 2016, Volume 80, Issue 4, Pages 123–130 (Mi izv8392)  

This article is cited in 3 scientific papers (total in 3 papers)

Local zeta factors and geometries under $\operatorname{Spec}\mathbf Z$

Yu. I. Manin

Max Planck Institute for Mathematics

Abstract: The first part of this note shows that the odd-period polynomial of each Hecke cusp eigenform for the full modular group produces via the Rodriguez-Villegas transform ([1]) a polynomial satisfying the functional equation of zeta type and having non-trivial zeros only in the middle line of its critical strip. The second part discusses the Chebyshev lambda-structure of the polynomial ring as Borger's descent data to $\mathbf{F}_1$ and suggests its role in a possible relation of the $\Gamma_{\mathbf{R}}$-factor to ‘real geometry over $\mathbf{F}_1$’ (cf. [2]).

Keywords: cusp forms, period polynomials, local factors.

DOI: https://doi.org/10.4213/im8392

Full text: PDF file (419 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2016, 80:4, 751–758

Bibliographic databases:

UDC: 511.334
MSC: 11F67
Received: 20.04.2015
Revised: 01.09.2015
Language:

Citation: Yu. I. Manin, “Local zeta factors and geometries under $\operatorname{Spec}\mathbf Z$”, Izv. RAN. Ser. Mat., 80:4 (2016), 123–130; Izv. Math., 80:4 (2016), 751–758

Citation in format AMSBIB
\Bibitem{Man16}
\by Yu.~I.~Manin
\paper Local zeta factors and geometries under $\operatorname{Spec}\mathbf Z$
\jour Izv. RAN. Ser. Mat.
\yr 2016
\vol 80
\issue 4
\pages 123--130
\mathnet{http://mi.mathnet.ru/izv8392}
\crossref{https://doi.org/10.4213/im8392}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3535360}
\zmath{https://zbmath.org/?q=an:06640629}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2016IzMat..80..751M}
\elib{http://elibrary.ru/item.asp?id=26414239}
\transl
\jour Izv. Math.
\yr 2016
\vol 80
\issue 4
\pages 751--758
\crossref{https://doi.org/10.1070/IM8392}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000384882700006}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84987653222}


Linking options:
  • http://mi.mathnet.ru/eng/izv8392
  • https://doi.org/10.4213/im8392
  • http://mi.mathnet.ru/eng/izv/v80/i4/p123

    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. L. Le Bruyn, “Linear recursive sequences and $\mathrm{Spec}(\mathbb Z)$ over $\mathbb F_1$”, Comm. Algebra, 45:7 (2017), 3150–3158  crossref  mathscinet  zmath  isi  scopus
    2. S. Löbrich, W. J. Ma, J. Thorner, “Special values of motivic $L$-functions and zeta-polynomials for symmetric powers of elliptic curves”, Res. Math. Sci., 4 (2017), 26, 16 pp.  crossref  mathscinet  zmath  isi  scopus
    3. K. Ono, L. Rolen, F. Sprung, “Zeta-polynomials for modular form periods”, Adv. Math., 306 (2017), 328–343  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:295
    References:36
    First page:47

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