$θ(t) := \sum_{n=-∞}^∞ e^{−πn^2t}$ for $t > 0$.
(a) prove that $\int_1^∞ |θ(t)−1|^p dt $ is fintite for all $p>0$
(b) there exists $C_p$ for $0<p<2$ such that $\int_0^1 |θ(t)|^p dt ≤ C_p$
I think I have to use symmetry of theta function but I don't know how to use it. On (a) I came out with it is equal to $\int_0^1(|θ(1/t)−1|^p t^{-2}) dt$ but I can't bound it to integrable function.