Abel's theorem in problems and solutions - School of Mathematics

186 Problems of Chapter 2
FIGURE 81 FIGURE 82
FIGURE 83
307. See Figure 84. Hint. During a turn around the point
varies by by (cf., 260(b)) and by
i.e., the value of the function is multiplied by –1.
FIGURE 84 FIGURE 85
308. a) See Figure 85. b) During a turn around the point
varies by and, during a turn around the point
by (cf., 260). Consequently around the point the
value of the function is multiplied by and around
the point by The required scheme is shown in Figure
86. c) See Figure 87 (the Riemann surface is shown in Figure 126).
309. Let a value be chosen at the point and be
another point. If and are two arbitrary continuous curves joining
and without crossing the cuts (Figure 88), then evidently the curve
can be continuously deformed into the curve without passing through
the branch points. Since the function possesses the monodromy