On factors of automorphy of fractional weight for cocompact Fuchsian groups (Q1898241)

The group \(\text{PSL} (2, \mathbb{R})\) has fundamental group \(\mathbb{Z}\) and so has connected covering groups of order \(n\) for any \(n\). It is an important question to understand how these coverings behave when restricted to a Fuchsian group. In this paper the author rediscovers some results in this direction that had been known to Petersson and have been rediscovered many time since -- for some details see the reviewer's paper [Glasg. Math. J. 16, 123-140 (1975; Zbl 0317.20029)]. In this paper the author uses an interesting method based on the Riemann-Roch theorem.