Geodesic
On the zeta-functions of systems of quadratic forms
Matematičeskie zametki, Tome 20 (1976) no. 1, pp. 27-34 
A. N. Andrianov. On the zeta-functions of systems of quadratic forms. Matematičeskie zametki, Tome 20 (1976) no. 1, pp. 27-34. http://geodesic.mathdoc.fr/item/MZM_1976_20_1_a3/
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     author = {A. N. Andrianov},
     title = {On the zeta-functions of systems of quadratic forms},
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     pages = {27--34},
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     volume = {20},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_20_1_a3/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We prove that the zeta-function of $m$ variables of a system of $m$ positive-definite quadratic forms has a meromorphic analytic continuation onto the whole $m$-dimensional complex space.