Vanishing thetanulls for some dihedral and cyclic coverings of Riemann surfaces (Q2386858)

The author considers lifting properties for linear series of divisors under normal coverings of compact Riemann surfaces with cyclic or dihedral covering groups. After collecting some more or less known facts, the author treats mainly the question under which conditions there is a linear series on the base surface lifting to canonical divisors on the covering space. Thm. 3.1 and Thm. 6.1 give complete answers in the cases of dihedral and cyclic coverings with a prime number of sheets. Some other interesting results concern implications on Weierstrass points, half--canonical series (whose double are canonical) and trigonal coverings of elliptic curves.