Decoupling inequalities for short generalized Dirichlet sequences

We study decoupling theory for functions on $ℝ$ with Fourier transform supported in a neighborhood of short Dirichlet sequences ${\{\log <!--FUNCTION\; APPLICATION-->n\}}_{n=N+1}^{N+N^{1∕2}}$, as well as sequences with similar convexity properties. We utilize the wave packet structure of functions with frequency support near an arithmetic progression.