SHIFTED MOMENTS OF L-FUNCTIONS AND MOMENTS OF THETA FUNCTIONS

Assuming the Riemann Hypothesis, Soundararajan [Ann. of Math. (2) 170 (2009), 981-993] showed that (T)(integral o) vertical bar zeta (1/2 + it)vertical bar(2k) << T (log T)k(2)+epsilon. His method was used by Chandee [Q. 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 L-functions which allow us to derive upper bounds for moments of theta functions.