Abstract
Let S be a trigonal Riemann surface of genus g (> 4) and of the nth kind. It is known that there are two types of total (resp. ordinary) ramification points of the trigonal covering. At first, we give a criterion for deciding the kinds and types of ramification points in terms of a defining equation of a Riemann surface. Next, we show the existence of various types of ramification points. Thirdly, we give some estimates on the numbers of ramification points which include the assertion that there always exists an ordinary ramification point of type I unless S is cyclic trigonal.
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