Zapiski Nauchnykh Seminarov POMI, Automorphic functions and number theory. Part III, Tome 162 (1987), pp. 43-76
Citer cet article
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/
@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},
year = {1987},
volume = {162},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1987_162_a1/}
}
TY - JOUR
AU - A. I. Vinogradov
TI - Analytic continuation of $\zeta_3(s,k)$ in the critical strip. Arithmetical part
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1987
SP - 43
EP - 76
VL - 162
UR - http://geodesic.mathdoc.fr/item/ZNSL_1987_162_a1/
LA - ru
ID - ZNSL_1987_162_a1
ER -
%0 Journal Article
%A A. I. Vinogradov
%T Analytic continuation of $\zeta_3(s,k)$ in the critical strip. Arithmetical part
%J Zapiski Nauchnykh Seminarov POMI
%D 1987
%P 43-76
%V 162
%U http://geodesic.mathdoc.fr/item/ZNSL_1987_162_a1/
%G ru
%F ZNSL_1987_162_a1
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 $SL_3(Z)$.
