Download or read book Value Distribution in P Adic Analysis written by Alain Escassut and published by World Scientific. This book was released on 2015-11-27 with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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."--
Download or read book Value Distribution In P adic Analysis written by Alain Escassut and published by World Scientific. This book was released on 2015-11-27 with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Some Topics on Value Distribution and Differentiability in Complex and P adic Analysis written by Alain Escassut and published by . This book was released on 2008 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Advances in Ultrametric Analysis written by Alain Escassut and published by American Mathematical Soc.. This book was released on 2018-03-26 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Articles included in this book feature recent developments in various areas of non-Archimedean analysis: summation of -adic series, rational maps on the projective line over , non-Archimedean Hahn-Banach theorems, ultrametric Calkin algebras, -modules with a convex base, non-compact Trace class operators and Schatten-class operators in -adic Hilbert spaces, algebras of strictly differentiable functions, inverse function theorem and mean value theorem in Levi-Civita fields, ultrametric spectra of commutative non-unital Banach rings, classes of non-Archimedean Köthe spaces, -adic Nevanlinna theory and applications, and sub-coordinate representation of -adic functions. Moreover, a paper on the history of -adic analysis with a comparative summary of non-Archimedean fields is presented. Through a combination of new research articles and a survey paper, 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.
Download or read book p adic Numbers p adic Analysis and Zeta Functions written by Neal Koblitz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition of this work has become the standard introduction to the theory of p-adic numbers at both the advanced undergraduate and beginning graduate level. This second edition includes a deeper treatment of p-adic functions in Ch. 4 to include the Iwasawa logarithm and the p-adic gamma-function, the rearrangement and addition of some exercises, the inclusion of an extensive appendix of answers and hints to the exercises, as well as numerous clarifications.
Download or read book p adic Numbers written by Fernando Q. Gouvêa and published by Springer Nature. This book was released on 2020-06-19 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Analysis Probability Applications and Computation written by Karl‐Olof Lindahl and published by Springer. This book was released on 2019-04-29 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Harmonic Wavelet and P Adic Analysis written by N. M. Chuong and published by World Scientific. This book was released on 2007 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Value Distribution of L Functions written by Jr̲n Steuding and published by Springer Science & Business Media. This book was released on 2007-06-06 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Advances in Ultrametric Analysis written by Khodr Shamseddine and published by American Mathematical Soc.. This book was released on 2013 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book P adic Analytic Functions written by Alain Escassut and published by World Scientific. This book was released on 2021-03-17 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book P adic Analysis and Mathematical Physics written by Vasili? Sergeevich Vladimirov and published by World Scientific. This book was released on 1994 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: p-adic numbers play a very important role in modern number theory, algebraic geometry and representation theory. Lately p-adic numbers have attracted a great deal of attention in modern theoretical physics as a promising new approach for describing the non-Archimedean geometry of space-time at small distances.This is the first book to deal with applications of p-adic numbers in theoretical and mathematical physics. It gives an elementary and thoroughly written introduction to p-adic numbers and p-adic analysis with great numbers of examples as well as applications of p-adic numbers in classical mechanics, dynamical systems, quantum mechanics, statistical physics, quantum field theory and string theory.
Download or read book Advances in Non Archimedean Analysis written by Jesus Araujo-Gomez and published by American Mathematical Soc.. This book was released on 2011 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: These collected articles feature recent developments in various areas of non-Archimedean analysis: Hilbert and Banach spaces, finite dimensional spaces, topological vector spaces and operator theory, strict topologies, spaces of continuous functions and of strictly differentiable functions, isomorphisms between Banach functions spaces, and measure and integration.
Download or read book Value Distribution Theory Related to Number Theory written by Pei-Chu Hu and published by Springer Science & Business Media. This book was released on 2006-10-06 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Value Distribution Theory and Complex Dynamics written by William Cherry and published by American Mathematical Soc.. This book was released on 2002 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains six detailed papers written by participants of the special session on value distribution theory and complex dynamics held in Hong Kong at the First Joint International Meeting of the AMS and the Hong Kong Mathematical Society in December 2000. It demonstrates the strong interconnections between the two fields and introduces recent progress of leading researchers from Asia. In the book, W. Bergweiler discusses proper analytic maps with one critical point andgeneralizes a previous result concerning Leau domains. W. Cherry and J. Wang discuss non-Archimedean analogs of Picard's theorems. P.-C. Hu and C.-C. Yang give a survey of results in non-Archimedean value distribution theory related to unique range sets, the $abc$-conjecture, and Shiffman's conjecture.L. Keen and J. Kotus explore the dynamics of the family of $f \lambda(z)=\lambda\tan(z)$ and show that it has much in common with the dynamics of the familiar quadratic family $f c(z)=z2+c$. R. Oudkerk discusses the interesting phenomenon known as parabolic implosion and, in particular, shows the persistence of Fatou coordinates under perturbation. Finally, M. Taniguchi discusses deformation spaces of entire functions and their combinatorial structure of singularities of the functions. The bookis intended for graduate students and research mathematicians interested in complex dynamics, function theory, and non-Archimedean function theory.
Download or read book Analytic Elements in P adic Analysis written by Alain Escassut and published by World Scientific. This book was released on 1995 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is probably the first book dedicated to this topic. The behaviour of the analytic elements on an infraconnected set D in K an algebraically closed complete ultrametric field is mainly explained by the circular filters and the monotonous filters on D, especially the T-filters: zeros of the elements, Mittag-Leffler series, factorization, Motzkin factorization, maximum principle, injectivity, algebraic properties of the algebra of the analytic elements on D, problems of analytic extension, factorization into meromorphic products and connections with Mittag-Leffler series. This is applied to the differential equation y'=hy (y, h analytic elements on D), analytic interpolation, injectivity, and to the p-adic Fourier transform.
Download or read book Distribution Theory of Algebraic Numbers written by Pei-Chu Hu and published by Walter de Gruyter. This book was released on 2008-12-10 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book timely surveys new research results and related developments in Diophantine approximation, a division of number theory which deals with the approximation of real numbers by rational numbers. The book is appended with a list of challenging open problems and a comprehensive list of references. From the contents: Field extensions • Algebraic numbers • Algebraic geometry • Height functions • The abc-conjecture • Roth's theorem • Subspace theorems • Vojta's conjectures • L-functions.
