A note on functional equations for zeta functions with values in Chow motives

Franziska Heinloth[1]

  • [1] Universität Duisburg—Essen Standort Essen FB6, Mathematik 45117 Essen (German)

Annales de l’institut Fourier (2007)

  • Volume: 57, Issue: 6, page 1927-1945
  • ISSN: 0373-0956

Abstract

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We consider zeta functions with values in the Grothendieck ring of Chow motives. Investigating the λ –structure of this ring, we deduce a functional equation for the zeta function of abelian varieties. Furthermore, we show that the property of having a rational zeta function satisfying a functional equation is preserved under products.

How to cite

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Heinloth, Franziska. "A note on functional equations for zeta functions with values in Chow motives." Annales de l’institut Fourier 57.6 (2007): 1927-1945. <http://eudml.org/doc/10282>.

@article{Heinloth2007,
abstract = {We consider zeta functions with values in the Grothendieck ring of Chow motives. Investigating the $\lambda $–structure of this ring, we deduce a functional equation for the zeta function of abelian varieties. Furthermore, we show that the property of having a rational zeta function satisfying a functional equation is preserved under products.},
affiliation = {Universität Duisburg—Essen Standort Essen FB6, Mathematik 45117 Essen (German)},
author = {Heinloth, Franziska},
journal = {Annales de l’institut Fourier},
keywords = {zeta functions; Chow motives; functional equation},
language = {eng},
number = {6},
pages = {1927-1945},
publisher = {Association des Annales de l’institut Fourier},
title = {A note on functional equations for zeta functions with values in Chow motives},
url = {http://eudml.org/doc/10282},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Heinloth, Franziska
TI - A note on functional equations for zeta functions with values in Chow motives
JO - Annales de l’institut Fourier
PY - 2007
PB - Association des Annales de l’institut Fourier
VL - 57
IS - 6
SP - 1927
EP - 1945
AB - We consider zeta functions with values in the Grothendieck ring of Chow motives. Investigating the $\lambda $–structure of this ring, we deduce a functional equation for the zeta function of abelian varieties. Furthermore, we show that the property of having a rational zeta function satisfying a functional equation is preserved under products.
LA - eng
KW - zeta functions; Chow motives; functional equation
UR - http://eudml.org/doc/10282
ER -

References

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