@article{Stein, author = {Stein, Oliver}, title = {Analytic properties of eisenstein series and standard L-Functions}, series = {Nagoya mathematical Journal}, volume = {244}, journal = {Nagoya mathematical Journal}, publisher = {CAMBRIDGE UNIV PRESS}, doi = {10.1017/nmj.2020.11}, pages = {168 -- 203}, abstract = {We prove a functional equation for a vector valued real analytic Eisenstein series transforming with the Weil representation of Sp(n, Z) on C[(L'/L)(n)]. By relating such an Eisenstein series with a real analytic Jacobi Eisenstein series of degree n, a functional equation for such an Eisenstein series is proved. Employing a doubling method for Jacobi forms of higher degree established by Arakawa, we transfer the aforementioned functional equation to a zeta function defined by the eigenvalues of a Jacobi eigenform. Finally, we obtain the analytic continuation and a functional equation of the standard L-function attached to a Jacobi eigenform, which was already proved by Murase, however in a different way.}, language = {en} }