Geodesic
On Epstein's zeta-function
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 18, Tome 286 (2002), pp. 169-178 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $Q(x_1,x_2,x_3)=x^2_1+x^2_2+x^2_3$, and let $\zeta(s;Q)$ be Epstein's zeta-function of the form $Q$. It is proved that for $|t|>C>0$ one has the estimate $$ \zeta(1+it;Q)\ll|t|^{1/4+\varepsilon}. $$ 
@article{ZNSL_2002_286_a12,
     author = {O. M. Fomenko},
     title = {On {Epstein's} zeta-function},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {169--178},
     year = {2002},
     volume = {286},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2002_286_a12/}
}
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O. M. Fomenko. On Epstein's zeta-function. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 18, Tome 286 (2002), pp. 169-178. http://geodesic.mathdoc.fr/item/ZNSL_2002_286_a12/