A note on functional equations for zeta functions with values in Chow motives  [ Sur l’équation fonctionnelle des fonctions zêta à valeurs dans les motifs de Chow ]
Annales de l'Institut Fourier, Tome 57 (2007) no. 6, p. 1927-1945
Nous considérons les fonctions zêta à valeurs dans l’anneau de Grothendieck des motifs de Chow. L’étude de la λ-structure de cet anneau, nous permet d’obtenir une équation fonctionnelle pour la fonction zêta des variétés abéliennes. En outre nous montrons que l’existence d’une telle équation fonctionnelle est une propriété stable par produit.
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.
DOI : https://doi.org/10.5802/aif.2318
Classification:  14G10,  14F42
Mots clés: fonctions zêta, motifs de Chow, équation fonctionnelle
@article{AIF_2007__57_6_1927_0,
     author = {Heinloth, Franziska},
     title = {A note on functional equations for zeta functions with values in Chow motives},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {57},
     number = {6},
     year = {2007},
     pages = {1927-1945},
     doi = {10.5802/aif.2318},
     mrnumber = {2377891},
     zbl = {1154.14018},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2007__57_6_1927_0}
}
Heinloth, Franziska. A note on functional equations for zeta functions with values in Chow motives. Annales de l'Institut Fourier, Tome 57 (2007) no. 6, pp. 1927-1945. doi : 10.5802/aif.2318. http://www.numdam.org/item/AIF_2007__57_6_1927_0/

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