This work is about a generalization of Kœcher’s zeta function. Let $V$ be an Euclidean simple Jordan algebra of dimension $n$ and rank $m$, $E$ an Euclidean space of dimension $N$, $\varphi$ a regular self-adjoint representation of $V$ in $E$, $Q$ the quadratic form associated to $\varphi$, $\Omega$ the symmetric cone associated to $V$ and $G\left(\Omega \right)$ its automorphism group$$G\left(\Omega \right)=\{g\in GL(V\left)\right|g\left(\Omega \right)=\Omega \}.$$($H_1$) Assume that $V$ and $E$ have $\mathbf{Q}$-structures $V_{\mathbf{Q}}$ and $E_{\mathbf{Q}}$ respectively and $\varphi$ is defined over $\mathbf{Q}$. Let $L$ be a lattice in $E_{\mathbf{Q}}$. The zeta series associated to $\varphi$ and $L$ is defined by$${\zeta }_L\left(s\right)=\sum _{l\in {\Gamma }_{\circ }\setminus L^{\text{'}}}\left[\det \right(Q\left(l\right)){]}^{-s},\forall s\in \mathbf{C}$$where $L^{\text{'}}=\{l\in L|\det \left(Q\right(l\left)\right)\ne 0\}$,...