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We study decoupling theory for functions on $\mathbb{R}$ with Fouriertransform supported in a neighborhood of short Dirichlet sequences $\{\logn\}_{n=N+1}^{N+N^{1/2}}$, as well as sequences with similar convexityproperties. We utilize the wave packet structure of functions with frequencysupport near an arithmetic progression.

Decoupling inequalities for short generalized Dirichlet sequences