Geodesic
Analytic continuation of $\zeta_3(s,k)$ in the critical strip. Arithmetical part
Zapiski Nauchnykh Seminarov POMI, Automorphic functions and number theory. Part III, Tome 162 (1987), pp. 43-76

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In this paper we study the zeta-function $$ \zeta_3(s,k)=\sum^\infty_{n=1}\frac{\tau_3(n)\tau_3(n+k)}{(\sqrt{n(n+k)})^s} $$ with the help of the technique of automorphic functions for $SL_3(Z)$. 
@article{ZNSL_1987_162_a1,
     author = {A. I. Vinogradov},
     title = {Analytic continuation of $\zeta_3(s,k)$ in the critical strip. {Arithmetical} part},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {43--76},
     publisher = {mathdoc},
     volume = {162},
     year = {1987},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1987_162_a1/}
}
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A. I. Vinogradov. Analytic continuation of $\zeta_3(s,k)$ in the critical strip. Arithmetical part. Zapiski Nauchnykh Seminarov POMI, Automorphic functions and number theory. Part III, Tome 162 (1987), pp. 43-76. http://geodesic.mathdoc.fr/item/ZNSL_1987_162_a1/