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Gp . Each nontrivial element y of G is loxodromic. , Cp' is a fundamental region for G called a standard fundamental region belonging to the generators ^ , . . , ^ . ) The region of discontinuity Ω of G is connected. The limit set Λ of G is a perfect, totally disconnected set of measure 0 if p > 1, consists of two points if p = 1, and is empty if p = 0 and G trivial. From now on we assume that p is fixed and p > 1, unless the converse is stated specifically. The results stated above are classical (see Appell, Goursat, and Fatou [6], Ford [16], Ahlfors and Sario [2]).

The solid foundation of traditional efforts will always help us to reach new horizons if we adopt the progressive point of view. REFERENCES 1. S. ULAM, The applicability of mathematics, in "Mathematical Sciences, a Collection of Essays," MIT Press, Cambridge, 1969. 2. H. WEYL, Relativity theory as a stimulus in mathematical research, Proc. Amer. Phil. Soc. 93(1949), 535. 22 C. C· LIN 3. ALBERT EINSTEIN, "Out of my Later Years," Philosophical Library, New York, 1950. 4. T . VON KARMAN AND C. C. L I N , On the existence of an exact solution of the equations of Navier-Stokes, Comm.

The number theorist is in the final analysis interested in the integer solutions of a set of equations, but over the years he has developed great insight into how to localize such problems to each prime and then put the local information together again. For him the field Zp , of the integers mod p, is therefore of profound interest, and he has by now a large body of algebraic information about it. , we can define the protective space kPn of dim n for every field k> just as we did before by taking as points of kPn the rays in kn+1.

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