The Set where a Transcendental Entire Function is Large and an Allied Problem |
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angular measure best possible Caratheodory's theorem Chebychev choose circular symmetrisation compact subsets conformal mapping converges uniformly denote the number desired entire function E₁(R E₁(RK Edrei entire function f(z f(rei f(rz₁ F₁ finite order fixed real number Fuchs and Shea function of finite function of order harmonic measure holomorphic i>io identity map inf log M(r,f infinite product integer leading coefficient unity Lemma Let f(z lim inf log log ½ log Rk log+ log|w₁ maps G conformally maximum modulus meromorphic function Möbius map n₁ log number of zeros O(a² O(log open arc open set order of g(z P1 lim sup Pk z/Rk polynomial Presidency College Proof R₁ reio Riemann mapping theorem Riemann Sphere Rk,f S₁ US2 sequence of circles spread conjecture Subinoy Chakravarty sufficiently large transcendental entire function w(z₁ W₁ z₁ zero order zeros of g₁(z λθο λπ πιλ