Non-weight modules over gap-p Virasoro algebras

In this paper, we study non-weight modules over gap-p Virasoro algebras, including Whittaker modules, U(C L₀)-free modules and their tensor products. We establish necessary and sufficient conditions for universal Whittaker modules to be irreducible and study the structure of irreducible Whittaker modules. The U(C L₀)-free modules of rank 1 are classified and the irreducibility of such modules are determined. Moreover, the irreducibility of tensor products of U(C L₀)-free modules of rank 1 and irreducible restricted modules is also determined.