Meromorphic Functions over Non-Archimedean Fields

AvPei-Chu Hu,Chung-Chun Yang

Inbunden, Engelska, 2000

Del i serien Mathematics and Its Applications

536 kr

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Beskrivning

This book introduces value distribution theory over non-Archimedean fields, starting with a survey of two Nevanlinna-type main theorems and defect relations for meromorphic functions and holomorphic curves. Secondly, it gives applications of the above theory to, for example, abc-conjecture, Waring's problem, uniqueness theorems for meromorphic functions, and Malmquist-type theorems for differential equations over non-Archimedean fields. Next, iteration theory of rational and entire functions over non-Archimedean fields and Schmidt's subspace theorems are studied. Finally, the book suggests some new problems for further research.

Produktinformation

Utgivningsdatum:2000-09-30
Mått:160 x 241 x 22 mm
Vikt:629 g
Format:Inbunden
Språk:Engelska
Serie:Mathematics and Its Applications
Antal sidor:295
Upplaga:2000
Förlag:Kluwer Academic Publishers
ISBN:9780792365327

Utforska kategorier

Beräkning och matematisk analys inom Naturvetenskap och teknik

Innehållsförteckning

1 Basic facts in p-adic analysis.- 1.1 p-adic numbers.- 1.2 Field extensions.- 1.3 Maximum term of power series.- 1.4 Weierstrass preparation theorem.- 1.5 Newton polygons.- 1.6 Non-Archimedean meromorphic functions.- 2 Nevanlinna theory.- 2.1 Characteristic functions.- 2.2 Growth estimates of meromorphic functions.- 2.3 Two main theorems.- 2.4 Notes on the second main theorem.- 2.5 ‘abc’ conjecture over function fields.- 2.6 Waring’s problem over function fields.- 2.7 Exponent of convergence of zeros.- 2.8 Value distribution of differential polynomials.- 3 Uniqueness of meromorphic functions.- 3.1 Adams-Straus’ uniqueness theorems.- 3.2 Multiple values of meromorphic functions.- 3.3 Uniqueness polynomials of meromorphic functions.- 3.4 Unique range sets of meromorphic functions.- 3.5 The Frank-Reinders’ technique.- 3.6 Some urscm for M(?) and A(?).- 3.7 Some ursim for meromorphic functions.- 3.8 Unique range sets for multiple values.- 4 Differential equations.- 4.1 Malmquist-type theorems.- 4.2 Generalized Malmquist-type theorems.- 4.3 Further results on Malmquist-type theorems.- 4.4 Admissible solutions of some differential equations.- 4.5 Differential equations of constant coefficients.- 5 Dynamics.- 5.1 Attractors and repellers.- 5.2 Riemann-Hurwitz relation.- 5.3 Fixed points of entire functions.- 5.4 Normal families.- 5.5 Montel’s theorems.- 5.6 Fatou-Julia theory.- 5.7 Properties of the Julia set.- 5.8 Iteration of z ? zd.- 5.9 Iteration of z ? z2 + c.- 6 Holomorphic curves.- 6.1 Multilinear algebra.- 6.2 The first main theorem of holomorphic curves.- 6.3 The second main theorem of holomorphic curves.- 6.4 Nochka weight.- 6.5 Degenerate holomorphic curves.- 6.6 Uniqueness of holomorphic curves.- 6.7 Second main theorem for hypersurfaces.- 6.8Holomorphic curves into projective varieties.- 7 Diophantine approximations.- 7.1 Schmidt’s subspace theorems.- 7.2 Vojta’s conjecture.- 7.3 General subspace theorems.- 7.4 Ru-Vojta’s subspace theorem for moving targets.- 7.5 Subspace theorem for degenerate mappings.- A The Cartan conjecture for moving targets.- A.1 Non-degenerate holomorphic curves.- A.2 The Steinmetz lemma.- A.3 A defect relation for moving targets.- A.4 The Ru-Stoll techniques.- A.5 Growth of the Steinmetz-Stoll mappings.- A.6 Moving targets in subgeneral position.- A.7 Moving targets in general position.- Symbols.