Geodesic
The zeta-function of a convolution
Zapiski Nauchnykh Seminarov POMI, Modular functions and quadratic forms. Part 1, Tome 183 (1990), pp. 22-48 Cet article a éte moissonné depuis la source Math-Net.Ru

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The zeta function of a convolution $\zeta_k(s)=\sum\limits_{n=1}^\infty\frac{\tau(n)\tau(n+k)}{n^s}$ (it converges absolutely for $\mathrm{Re}\, s>1$) can be extended to a meromorphic function on the entire $s$-plane. 
@article{ZNSL_1990_183_a1,
     author = {A. I. Vinogradov},
     title = {The zeta-function of a convolution},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {22--48},
     year = {1990},
     volume = {183},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1990_183_a1/}
}
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A. I. Vinogradov. The zeta-function of a convolution. Zapiski Nauchnykh Seminarov POMI, Modular functions and quadratic forms. Part 1, Tome 183 (1990), pp. 22-48. http://geodesic.mathdoc.fr/item/ZNSL_1990_183_a1/