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By Hardy G. H.

Hardy's natural arithmetic has been a vintage textbook for the reason that its ebook in1908. This reissue will convey it to the eye of a complete new new release of mathematicians.

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R^i <0(t/" 2(«,)>T ,T">*. } . 2) yields H H (9(UHH,TH,T )&m = 0. (9(U ),TH),T )&,=0. 7) )' we get [U«,T*] + VmT» = ^ fc(^) "V ds J at SM = VWU». 9) '*» | ' and the assertion follows. 2. Let F: T1,0M —* IR+ be a weakly Kahler Finsler metric on a com­ plex manifold M, and let a: [a, b] —> M be a regular curve with F(a) = CQ > 0. 6). 3. Let F: T ' M - » R be a weakly Kahler Finsler metric on a complex manifold M. Then for any p e M and v e Mp with F(v) = 1 there exists a unique geodesic a: {—e,e) —> M such that

M. Abate and G. Patrizio, Uniqueness of complex geodesies and characterization of circular domains, Man. Math. 74 (1992), 277-297. 3. M. Abate and G. Patrizio, Holomorphic curvature of Finsler metrics and com­ plex geodesies, to appear in J. Geom. Anal. 4. M. Abate and G. Patrizio, Complex geodesies and Finsler metrics, to appear in Proceedings of the Semester in Complex Analysis, Banach Center, Warsaw, 1992 5. M. Abate and G. Patrizio, A global approach to Finsler metrics, in preparation. 6. L.

2. 7) yields (Q{ (n(X,K)x,x) X,K)x,x) = 2cG(x,K)---{T(THH(X,X),K). = 2cG(x,*:> (X,X),K). 8) // Subtracting ( r ( x , x). K) = ( ^ ( x . 4) holds. 6). 5. Let F: Tl'°M —> 1 + be a strongly pseudoconvex Finsler metric on a complex manifold M with constant holomorphic curvature 1c € M. 2) holds. 9) for all H, K e H. 10) for allH, K G H. Proof: Take V, W € V such that 9 ( F ) = # and B{W) = if and extend them in any way to sections of V (and thus extend H and K as sections of H via Q). 2. 9). 3. □ So we have obtained one of the hermitian product terms.

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