On Periodic Meromorphic Functions

The first section of the note centres round the problem of constructing a periodic meromorphic function, with assigned poles and principal parts thereat, in a period strip. The second deals with rational functions of exp (2π^iz/λ), the main theorem of the section giving a necessary and sufficient condition for a periodic meromorphic function to be such a rational function, in terms of its Nevanlinna characteristic function. Throughout it is supposed, for the sake of simplicity, that λ is a positive number.