Hypercyclic Algebras for convolution operators of unimodular constant term

We study the existence of hypercyclic algebras for convolution operators $\mathrm{\Phi }(D)$ on the space of entire functions whose symbol $\mathrm{\Phi }$ has unimodular constant term. In particular, we provide new eigenvalue criteria for the existence of densely strongly algebrable sets of hypercyclic vectors.