Value Distribution in Ultrametric Analysis and Applications
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Book Overview After a construction of the complete ultrametric fields K, the book presents most of properties of analytic and meromorphic functions in ...
After a construction of the complete ultrametric fields K, the book presents most of properties of analytic and meromorphic functions in K: algebras of analytic elements, power series in a disk, order, type and cotype of growth of entire functions, clean functions, question on a relation true for clean functions, and a counter-example on a non-clean function. Transcendence order and transcendence type are examined with specific properties of certain p-adic numbers.
The Kakutani problem for the "corona problem" is recalled and multiplicative semi-norms are described. Problems on exponential polynomials, meromorphic functions are introduced and the Nevanlinna Theory is explained with its applications, particularly to problems of uniqueness. Injective analytic elements and meromorphic functions are examined and characterized through a relation.
The Nevanlinna Theory out of a hole is described. Many results on zeros of a meromorphic function and its derivative are examined, particularly the solution of the Hayman conjecture in a P-adic field is given. Moreover, if a meromorphic functions in all the field, admitting primitives, admit a Picard value, then it must have enormously many poles. Branched values are examined, with links to growth order of the denominator.
The Nevanlinna theory on small functions is explained with applications to uniqueness for a pair of meromorphic functions sharing a few small functions.
A short presentation in characteristic p is given with applications on Yoshida equation.
Book Details Format: Hardcover | Pages: 653 | Language: English | Publisher: WORLD SCIENTIFIC PUB CO INC | ISBN: 9811298327
FormatHardcover
Pages653
LanguageEnglish
ISBN9811298327
EAN9789811298325
PublisherWORLD SCIENTIFIC PUB CO INC
Publication Date2024-12-30
AccessoriesNo Accessory
ConditionNew
Product TypeHARD COVER BOOKS
Weight2.34 Pounds
Length9.0 Inches
Width6.0 Inches
Height1.44 Inches
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