%0 Journal Article
%T Subconvexity for a double Dirichlet series
%A Valentin Blomer
%J Mathematics
%D 2009
%I arXiv
%R 10.1112/S0010437X10004926
%X For Dirichlet series roughly of the type $Z(s, w) = sum_d L(s, chi_d) d^{-w}$ the subconvexity bound $Z(s, w) \ll (sw(s+w))^{1/6+\varepsilon}$ is proved on the critical lines $\Re s = \Re w = 1/2$. The convexity bound would replace 1/6 with 1/4. In addition, a mean square bound is proved that is consistent with the Lindel\"of hypothesis. An interesting specialization is $s=1/2$ in which case the above result give a subconvex bound for a Dirichlet series without an Euler product.
%U http://arxiv.org/abs/0907.4867v1