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Published online by Cambridge University Press: 24 October 2008
In his chapter on correspondences between algebraic curves Prof. Baker has raised a problem concerning the possibility, when we are given the equations of Hurwitz for a correspondence between two algebraic curves, of obtaining therefrom a reduction of the everywhere finite integrals on either curve into complementary regular defective systems of integrals. The problem is stated as an unproved theorem, an exact formulation of which is given below. The object of the present note is to give a proof of this theorem on the lines of Prof. Baker's chapter.
* Principles of geometry, vol. 6, Chapter i (Cambridge, 1933)Google Scholar; see, in particular, p. 66.
† When a matrix is denoted by a symbol such as a r, s the suffixes indicate that it is of type (r, s). 0r, s is the matrix of type (r, s) all of whose elements are zero, and 1r, r is the unit matrix of order r.
* See Baker, H. F., Journal London Math. Soc. 2, 10 (1935), 281Google Scholar, and references there given.