03195nam 2200601 450 99646686930331620220905221700.03-540-47146-410.1007/BFb0093846(CKB)1000000000437027(SSID)ssj0000327300(PQKBManifestationID)12083598(PQKBTitleCode)TC0000327300(PQKBWorkID)10298456(PQKB)11639402(DE-He213)978-3-540-47146-2(MiAaPQ)EBC5591389(Au-PeEL)EBL5591389(OCoLC)1066200145(MiAaPQ)EBC6841854(Au-PeEL)EBL6841854(PPN)155172905(EXLCZ)99100000000043702720220905d1990 uy 0engurnn|008mamaatxtccrTopics in Nevanlinna theory /Serge Lang, William Cherry1st ed. 1990.Berlin, Germany ;New York, New York :Springer,[1990]©19901 online resource (CLXXXIV, 180 p.) Lecture Notes in Mathematics,0075-8434 ;1433Bibliographic Level Mode of Issuance: Monograph3-540-52785-0 Includes bibliographical references (pages [169]-171) and index.Nevanlinna theory in one variable -- Equidimensional higher dimensional theory -- Nevanlinna Theory for Meromorphic Functions on Coverings of C -- Equidimensional Nevanlinna Theory on Coverings of Cn.These are notes of lectures on Nevanlinna theory, in the classical case of meromorphic functions, and the generalization by Carlson-Griffith to equidimensional holomorphic maps using as domain space finite coverings of C resp. Cn. Conjecturally best possible error terms are obtained following a method of Ahlfors and Wong. This is especially significant when obtaining uniformity for the error term w.r.t. coverings, since the analytic yields case a strong version of Vojta's conjectures in the number-theoretic case involving the theory of heights. The counting function for the ramified locus in the analytic case is the analogue of the normalized logarithmetic discriminant in the number-theoretic case, and is seen to occur with the expected coefficient 1. The error terms are given involving an approximating function (type function) similar to the probabilistic type function of Khitchine in number theory. The leisurely exposition allows readers with no background in Nevanlinna Theory to approach some of the basic remaining problems around the error term. It may be used as a continuation of a graduate course in complex analysis, also leading into complex differential geometry.Lecture notes in mathematics (Springer-Verlag) ;1433.Nevanlinna theoryNevanlinna theory.515Lang Serge1927-2005,1160Cherry William1966-MiAaPQMiAaPQMiAaPQBOOK996466869303316Topics in Nevanlinna Theory383042UNISA