Dynamics of Polynomials Over Local Fields PDF Download
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Author: Daniela Tataru
Publisher:
ISBN:
Category :
Languages : en
Pages : 101
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Author: Daniela Tataru
Publisher:
ISBN:
Category :
Languages : en
Pages : 101
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Author: Graham Everest
Publisher: Springer Science & Business Media
ISBN: 1447138988
Category : Mathematics
Languages : en
Pages : 217
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Book Description
The main theme of this book is the theory of heights as they appear in various guises. This includes a large body of results on Mahlers measure of the height of a polynomial. The authors'approach is very down to earth as they cover the rationals, assuming no prior knowledge of elliptic curves. The chapters include examples and particular computations, with all special calculation included so as to be self-contained. The authors devote space to discussing Mahlers measure and to giving some convincing and original examples to explain this phenomenon. XXXXXXX NEUER TEXT The main theme of this book is the theory of heights as it appears in various guises. To this §End.txt.Int.:, it examines the results of Mahlers measure of the height of a polynomial, which have never before appeared in book form. The authors take a down-to-earth approach that includes convincing and original examples. The book uncovers new and interesting connections between number theory and dynamics and will be interesting to researchers in both number theory and nonlinear dynamics.
Author: Joseph H. Silverman
Publisher: Springer Science & Business Media
ISBN: 1461208513
Category : Mathematics
Languages : en
Pages : 482
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Book Description
In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that "the theory of elliptic curves is rich, varied, and amazingly vast," and as a consequence, "many important topics had to be omitted." I included a brief introduction to ten additional topics as an appendix to the first volume, with the tacit understanding that eventually there might be a second volume containing the details. You are now holding that second volume. it turned out that even those ten topics would not fit Unfortunately, into a single book, so I was forced to make some choices. The following material is covered in this book: I. Elliptic and modular functions for the full modular group. II. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialization theorems. IV. Neron models, Kodaira-Neron classification of special fibers, Tate's algorithm, and Ogg's conductor-discriminant formula. V. Tate's theory of q-curves over p-adic fields. VI. Neron's theory of canonical local height functions.
Author: J.H. Silverman
Publisher: Springer Science & Business Media
ISBN: 038769904X
Category : Mathematics
Languages : en
Pages : 518
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This book provides an introduction to the relatively new discipline of arithmetic dynamics. Whereas classical discrete dynamics is the study of iteration of self-maps of the complex plane or real line, arithmetic dynamics is the study of the number-theoretic properties of rational and algebraic points under repeated application of a polynomial or rational function. A principal theme of arithmetic dynamics is that many of the fundamental problems in the theory of Diophantine equations have dynamical analogs.This graduate-level text provides an entry for students into an active field of research and serves as a standard reference for researchers.
Author: Asher N. Auel
Publisher:
ISBN:
Category :
Languages : en
Pages : 64
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Author: Dominique Cerveau
Publisher: American Mathematical Soc.
ISBN: 9780821832288
Category : Mathematics
Languages : en
Pages : 212
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Book Description
In the last twenty years, the theory of holomorphic dynamical systems has had a resurgence of activity, particularly concerning the fine analysis of Julia sets associated with polynomials and rational maps in one complex variable. At the same time, closely related theories have had a similar rapid development, for example the qualitative theory of differential equations in the complex domain. The meeting, ``Etat de la recherche'', held at Ecole Normale Superieure de Lyon, presented the current state of the art in this area, emphasizing the unity linking the various sub-domains. This volume contains four survey articles corresponding to the talks presented at this meeting. D. Cerveau describes the structure of polynomial differential equations in the complex plane, focusing on the local analysis in neighborhoods of singular points. E. Ghys surveys the theory of laminations by Riemann surfaces which occur in many dynamical or geometrical situations. N. Sibony describes the present state of the generalization of the Fatou-Julia theory for polynomial or rational maps in two or more complex dimensions. Lastly, the talk by J.-C. Yoccoz, written by M. Flexor, considers polynomials of degree $2$ in one complex variable, and in particular, with the hyperbolic properties of these polynomials centered around the Jakobson theorem. This is a general introduction that gives a basic history of holomorphic dynamical systems, demonstrating the numerous and fruitful interactions among the topics. In the spirit of the ``Etat de la recherche de la SMF'' meetings, the articles are written for a broad mathematical audience, especially students or mathematicians working in different fields. This book is translated from the French edition by Leslie Kay.
Author: Ernst-Wilhelm Zink
Publisher:
ISBN:
Category :
Languages : de
Pages : 36
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Author: Charles Favre
Publisher: Princeton University Press
ISBN: 0691235465
Category : Mathematics
Languages : en
Pages : 0
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Book Description
New mathematical research in arithmetic dynamics In The Arithmetic of Polynomial Dynamical Pairs, Charles Favre and Thomas Gauthier present new mathematical research in the field of arithmetic dynamics. Specifically, the authors study one-dimensional algebraic families of pairs given by a polynomial with a marked point. Combining tools from arithmetic geometry and holomorphic dynamics, they prove an “unlikely intersection” statement for such pairs, thereby demonstrating strong rigidity features for them. They further describe one-dimensional families in the moduli space of polynomials containing infinitely many postcritically finite parameters, proving the dynamical André-Oort conjecture for curves in this context, originally stated by Baker and DeMarco. This is a reader-friendly invitation to a new and exciting research area that brings together sophisticated tools from many branches of mathematics.
Author: L. Rédei
Publisher: Elsevier
ISBN: 1483257835
Category : Mathematics
Languages : en
Pages : 268
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Book Description
Lacunary Polynomials Over Finite Fields focuses on reducible lacunary polynomials over finite fields, as well as stem polynomials, differential equations, and gaussian sums. The monograph first tackles preliminaries and formulation of Problems I, II, and III, including some basic concepts and notations, invariants of polynomials, stem polynomials, fully reducible polynomials, and polynomials with a restricted range. The text then takes a look at Problem I and reduction of Problem II to Problem III. Topics include reduction of the marginal case of Problem II to that of Problem III, proposition on power series, proposition on polynomials, and preliminary remarks on polynomial and differential equations. The publication ponders on Problem III and applications. Topics include homogeneous elementary symmetric systems of equations in finite fields; divisibility maximum properties of the gaussian sums and related questions; common representative systems of a finite abelian group with respect to given subgroups; and difference quotient of functions in finite fields. The monograph also reviews certain families of linear mappings in finite fields, appendix on the degenerate solutions of Problem II, a lemma on the greatest common divisor of polynomials with common gap, and two group-theoretical propositions. The text is a dependable reference for mathematicians and researchers interested in the study of reducible lacunary polynomials over finite fields.
Author: Graham Everest
Publisher:
ISBN: 9781447138990
Category :
Languages : en
Pages : 228
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