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001 978-3-540-47146-2
003 DE-He213
005 20190213151806.0
007 cr nn 008mamaa
008 121227s1990 gw | s |||| 0|eng d
020 _a9783540471462
_9978-3-540-47146-2
024 7 _a10.1007/BFb0093846
_2doi
050 4 _aQA299.6-433
072 7 _aPBK
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aPBK
_2thema
082 0 4 _a515
_223
245 1 0 _aTopics in Nevanlinna Theory
_h[electronic resource] /
_cedited by Serge Lang, William Cherry.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c1990.
300 _aCLXXXIV, 180 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1433
505 0 _aNevanlinna theory in one variable -- Equidimensional higher dimensional theory -- Nevanlinna Theory for Meromorphic Functions on Coverings of C -- Equidimensional Nevanlinna Theory on Coverings of Cn.
520 _aThese 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.
650 0 _aGlobal analysis (Mathematics).
650 0 _aGlobal differential geometry.
650 0 _aGeometry, algebraic.
650 0 _aNumber theory.
650 1 4 _aAnalysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12007
650 2 4 _aDifferential Geometry.
_0http://scigraph.springernature.com/things/product-market-codes/M21022
650 2 4 _aAlgebraic Geometry.
_0http://scigraph.springernature.com/things/product-market-codes/M11019
650 2 4 _aNumber Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M25001
700 1 _aLang, Serge.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
700 1 _aCherry, William.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662213599
776 0 8 _iPrinted edition:
_z9783540527855
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1433
856 4 0 _uhttps://doi.org/10.1007/BFb0093846
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c11905
_d11905