Fonction zêta d’Epstein et dilogarithme de Bloch-Wigner

Bertin, Marie José

Journal de théorie des nombres de Bordeaux, Volume 23 (2011) no. 1, pp. 21-34.

We give an expression for $s=2$ of some normalized Epstein series as Bloch-Wigner dilogarithms of algebraic numbers of $\mathbb{Q}\left(\sqrt{\Delta }\right)$, for the discriminants $\Delta$ associated to the quadratic form.

Nous exprimons certaines séries d’Epstein normalisées en $s=2$ comme combinaisons linéaires de dilogarithmes de Bloch-Wigner en des nombres algébriques des corps $\mathbb{Q}\left(\sqrt{\Delta }\right)$ pour les discriminants $\Delta$ associés à la forme quadratique.

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