We prove functional equations for the absolute zeta functions. We also show that the absolute zeta functions satisfy the tensor structure in the sense that their singularities possess an additive property under the tensor product. Moreover those singularities satisfy the analog of the Riemann hypothesis.
Publié le : 2009-06-15
Classification:
Zeta functions,
the field with one element,
absolute mathematics,
11M41
@article{1244037801,
author = {Kim, Sojung and Koyama, Shin-ya and Kurokawa, Nobushige},
title = {The Riemann hypothesis and functional equations for zeta functions over ${\bf F}\_1}$},
journal = {Proc. Japan Acad. Ser. A Math. Sci.},
volume = {85},
number = {2},
year = {2009},
pages = { 75-80},
language = {en},
url = {http://dml.mathdoc.fr/item/1244037801}
}
Kim, Sojung; Koyama, Shin-ya; Kurokawa, Nobushige. The Riemann hypothesis and functional equations for zeta functions over ${\bf F}_1}$. Proc. Japan Acad. Ser. A Math. Sci., Tome 85 (2009) no. 2, pp. 75-80. http://gdmltest.u-ga.fr/item/1244037801/