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Abel's theorem and the allied theory, including the theory of the theta functions (1897)

Baker, H. F. (Henry Frederick), 1866-1956 · Cambridge : University Press · leaf 278

An illustration from Abel's theorem and the allied theory, including the theory of the theta functions, 1897, leaf 278
nient to dissect the Riemannsurface in such a way that the function log @ {v ^ + e) may be regarded assingle-valued on the dissected surface. Denoting the p zeros of © {v^- * -F e)by ^i, ..., ^^j we may suppose the dissection made by p closed curves such asthe one represented in Figure [2], so that… … p closed curves such as the one in the figure. For we proved that a com-plete circuit of the closed curve formed by the sides of the (a^, 6,.) period-loop-pair, gives an increment of 27ri for the function log © (u) ; when thesurface is dissected as in the figure this increment of 27ri is again…

Geometry, Algebraic · Functions, Theta

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