Riemann-Hilbert problem for automorphic functions and the Schottky-Klein prime function (Q2457874)

The construction of analogues of the Cauchy kernel is crucial for the solution of Riemann-Hilbert problems on compact Riemann surfaces. In the paper under review, a new formula for a quasi-automorphic analogue of the Cauchy kernel is derived. There are essentially used the results of the papers [\textit{L. I. Chibrikova} and \textit{V. V. Sil'vestrov}, Izv. Vyssh. Uchebn. Zaved., Mat. 1978, No. 12(199), 117--121 (1978; Zbl 0405.30032), Tr. Semin. Kraev. Zadacham 16, 202--217 (1979; Zbl 0449.30036)]. The obtained results are used for the solution of the Riemann-Hilbert problem with piecewise Hölder coefficient for symmetric automorphic functions.