WEIERSTRASS POINTS WITH FIRST TWO NON-GAPS EQUAL TO n AND n+2

We study Weierstrass points on a smooth curve C whose first two non-gaps equal n and n + 2. If the genus g of C satisfies g > [(n(2) - 1)/2], then it is known that C is a two-sheeted covering of a curve. In this paper, we mainly concentrate on a point P is an element of C such that vertical bar nP vertical bar is a base point free pencil and 1 (n + 2)P vertical bar is a base point free simple net, whence necessarily g <= [(n(2) - 1)/2], and study bounds for numbers of such Weierstrass points on C.