Defective dual varieties for real spectra

We introduce an invariant of a finite point configuration $A \subset $\mathbb{R}$^{1+n}$whichwedenotethecuspidalformof$A$. We use this invariant to extend Esterov’s characterization of dual defective point configurations to exponential sums; the dual variety associated to $A$ has codimension at least $2$ if and only if $A$ does not contain any iterated circuit.