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发帖数: 758 | 1 f and g are entire functions with f^2+g^2=1, prove that there exists an
entire function h such that f=cos(h), g=sin(h). | c*****n
发帖数: 33 | 2 Let S be the algebraic curve in C^2 defined by x^2+y^2=1, the p:C\to S, z->(
sin z,cos z) is a covering map (period 2\pi ). The map (f,g):C\to S\subset
C^2 is a holomorphic map. Note that C is simply connected, so the map (f,g)
can be lifted along the covering map p. Let h:C\to C be the lifting of (f,g
), then h is the entire function satisfying the requirement. |
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