Value Distribution In P Adic Analysis
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Value Distribution In P Adic Analysis
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Author : Alain Escassut
language : en
Publisher: World Scientific
Release Date : 2015-11-27
Value Distribution In P Adic Analysis written by Alain Escassut and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-27 with Mathematics categories.
"The book first explains the main properties of analytic functions in order to use them in the study of various problems in p-adic value distribution. Certain properties of p-adic transcendental numbers are examined such as order and type of transcendence, with problems on p-adic exponentials. Lazard's problem for analytic functions inside a disk is explained. P-adic meromorphics are studied. Sets of range uniqueness in a p-adic field are examined. The ultrametric Corona problem is studied. Injective analytic elements are characterized. The p-adic Nevanlinna theory is described and many applications are given: p-adic Hayman conjecture, Picard's values for derivatives, small functions, branched values, growth of entire functions, problems of uniqueness, URSCM and URSIM, functions of uniqueness, sharing value problems, Nevanlinna theory in characteristic p>0, p-adic Yosida's equation."--
Value Distribution In Ultrametric Analysis And Applications
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Author : Alain Escassut
language : en
Publisher: World Scientific
Release Date : 2024-12-20
Value Distribution In Ultrametric Analysis And Applications written by Alain Escassut and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-20 with Mathematics categories.
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.
Some Topics On Value Distribution And Differentiability In Complex And P Adic Analysis
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Author : Alain Escassut
language : en
Publisher:
Release Date : 2008
Some Topics On Value Distribution And Differentiability In Complex And P Adic Analysis written by Alain Escassut and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Complex analysis categories.
Value Distribution Of L Functions
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Author : Jörn Steuding
language : en
Publisher: Springer
Release Date : 2007-05-26
Value Distribution Of L Functions written by Jörn Steuding and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-26 with Mathematics categories.
These notes present recent results in the value-distribution theory of L-functions with emphasis on the phenomenon of universality. Universality has a strong impact on the zero-distribution: Riemann’s hypothesis is true only if the Riemann zeta-function can approximate itself uniformly. The text proves universality for polynomial Euler products. The authors’ approach follows mainly Bagchi's probabilistic method. Discussion touches on related topics: almost periodicity, density estimates, Nevanlinna theory, and functional independence.
P Adic Analytic Functions
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Author : Alain Escassut
language : en
Publisher: World Scientific
Release Date : 2021-03-17
P Adic Analytic Functions written by Alain Escassut and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-17 with Mathematics categories.
P-adic Analytic Functions describes the definition and properties of p-adic analytic and meromorphic functions in a complete algebraically closed ultrametric field.Various properties of p-adic exponential-polynomials are examined, such as the Hermite-Lindemann theorem in a p-adic field, with a new proof. The order and type of growth for analytic functions are studied, in the whole field and inside an open disk. P-adic meromorphic functions are studied, not only on the whole field but also in an open disk and on the complemental of an open disk, using Motzkin meromorphic products. Finally, the p-adic Nevanlinna theory is widely explained, with various applications. Small functions are introduced with results of uniqueness for meromorphic functions. The question of whether the ring of analytic functions—in the whole field or inside an open disk—is a Bezout ring is also examined.
Harmonic Wavelet And P Adic Analysis
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Author : Yu V Egorov
language : en
Publisher: World Scientific
Release Date : 2007-05-14
Harmonic Wavelet And P Adic Analysis written by Yu V Egorov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-14 with Mathematics categories.
The mutual influence between mathematics and science and technology is becoming more and more widespread with profound connections among them being discovered. In particular, important connections between harmonic analysis, wavelet analysis and p-adic analysis have been found recently.This volume reports these findings and guides the reader towards the latest areas for further research. It is divided into two parts: harmonic, wavelet and p-adic analysis and p-adic and stochastic analysis.
Value Distribution Theory Related To Number Theory
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Author : Pei-Chu Hu
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-10-06
Value Distribution Theory Related To Number Theory written by Pei-Chu Hu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-10-06 with Mathematics categories.
The subject of the book is Diophantine approximation and Nevanlinna theory. This book proves not just some new results and directions but challenging open problems in Diophantine approximation and Nevanlinna theory. The authors’ newest research activities on these subjects over the past eight years are collected here. Some of the significant findings are the proof of Green-Griffiths conjecture by using meromorphic connections and Jacobian sections, generalized abc-conjecture, and more.
Advances In Ultrametric Analysis
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Author : Khodr Shamseddine
language : en
Publisher: American Mathematical Soc.
Release Date : 2013
Advances In Ultrametric Analysis written by Khodr Shamseddine and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.
This volume contains papers based on lectures given at the 12th International Conference on p-adic Functional Analysis, which was held at the University of Manitoba on July 2-6, 2012. Through a combination of new research articles and survey papers, this book provides the reader with an overview of current developments and techniques in non-archimedean analysis as well as a broad knowledge of some of the sub-areas of this exciting and fast-developing research area.
Analysis Probability Applications And Computation
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Author : Karl‐Olof Lindahl
language : en
Publisher: Springer
Release Date : 2019-04-29
Analysis Probability Applications And Computation written by Karl‐Olof Lindahl and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-29 with Mathematics categories.
This book is a collection of short papers from the 11th International ISAAC Congress 2017 in Växjö, Sweden. The papers, written by the best international experts, are devoted to recent results in mathematics with a focus on analysis. The volume provides to both specialists and non-specialists an excellent source of information on the current research in mathematical analysis and its various interdisciplinary applications.
P Adic Numbers
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Author : Fernando Q. Gouvêa
language : en
Publisher: Springer Nature
Release Date : 2020-06-19
P Adic Numbers written by Fernando Q. Gouvêa and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-19 with Mathematics categories.
There are numbers of all kinds: rational, real, complex, p-adic. The p-adic numbers are less well known than the others, but they play a fundamental role in number theory and in other parts of mathematics. This elementary introduction offers a broad understanding of p-adic numbers. From the reviews: "It is perhaps the most suitable text for beginners, and I shall definitely recommend it to anyone who asks me what a p-adic number is." --THE MATHEMATICAL GAZETTE