Another proof and a sharpening of Huang´s theorem

Two further proofs of Huang´s theorem on the zeros of analytic functions of two variables are given: the first is similar to previous proofs, but is made shorter by the use of a known maximum-modulus principle; the second is completely different, using a theorem of Rudin which actually gives a sharper result than Huang´s. Finally, it is indicated how a correspondingly sharper result may be obtained in higher dimensions.