Local zeta factors and geometries under

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 criti...

Full description

Saved in:
Bibliographic Details
Published inIzvestiya. Mathematics Vol. 80; no. 4; pp. 751 - 758
Main Author Manin, Yu. I.
Format Journal Article
LanguageEnglish
Published London Mathematical Society, Turpion Ltd and the Russian Academy of Sciences 01.08.2016
Subjects
cusp forms
local factors
period polynomials
Online AccessGet full text

Cover

More Information
Summary: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 and suggests its role in a possible relation of the -factor to `real geometry over ' (cf. [2]).
ISSN:1064-5632
1468-4810
DOI:10.1070/IM8392