Shifted moments of l-functions and moments of theta functions

Assuming the Riemann Hypothesis, Soundararajan [Ann. of Math.a (2) 170 (2009), 981-993] showed that f^T₀ ℓ.1=2 C it/^2κ T .log T /^κk2+€ His method was used by Chandee [Q.A J. Math. 62 (2011), 545-572] to obtain upper bounds for shifted moments of the Riemann Zeta function. Building on these ideas of Chandee and Soundararajan, we obtain, conditionally, upper bounds for shifted moments of Dirichlet-functions which allow us to derive upper bounds for moments of theta functions.