The Lindelöf class of L-functions II

In 2002, the second author introduced a class of [Formula: see text]-functions [Formula: see text], which contains the Selberg class and forms a ring. In this paper, we study this class and prove that the invariant [Formula: see text], which is the generalization of degree in the Selberg class cannot take non-integer values between [Formula: see text] and [Formula: see text]. We also study the ring structure of [Formula: see text] showing that it is non-Noetherian.