Twists and resonance of L-functions, II

We investigate the analytic properties of nonlinear twists of $L$-functions. Given an $L$-function $F(s)$ of degree $d$ and a twist $F(s;f)$ with leading exponent $>1/d$, we first prove a general transformation formula relating $F(s;f)$ to its dual twist $overline{F}(s;f^*)$. Then we combine such a formula with the results obtained in part I of the paper, to deduce the analytic properties of new classes of nonlinear twists. This allows to detect several new cases of resonance for the classical $L$-functions.