Download or read book Capacity Theory on Algebraic Curves written by Robert S. Rumely and published by Springer. This book was released on 2006-11-14 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: Capacity is a measure of size for sets, with diverse applications in potential theory, probability and number theory. This book lays foundations for a theory of capacity for adelic sets on algebraic curves. Its main result is an arithmetic one, a generalization of a theorem of Fekete and Szegö which gives a sharp existence/finiteness criterion for algebraic points whose conjugates lie near a specified set on a curve. The book brings out a deep connection between the classical Green's functions of analysis and Néron's local height pairings; it also points to an interpretation of capacity as a kind of intersection index in the framework of Arakelov Theory. It is a research monograph and will primarily be of interest to number theorists and algebraic geometers; because of applications of the theory, it may also be of interest to logicians. The theory presented generalizes one due to David Cantor for the projective line. As with most adelic theories, it has a local and a global part. Let /K be a smooth, complete curve over a global field; let Kv denote the algebraic closure of any completion of K. The book first develops capacity theory over local fields, defining analogues of the classical logarithmic capacity and Green's functions for sets in (Kv). It then develops a global theory, defining the capacity of a galois-stable set in (Kv) relative to an effictive global algebraic divisor. The main technical result is the construction of global algebraic functions whose logarithms closely approximate Green's functions at all places of K. These functions are used in proving the generalized Fekete-Szegö theorem; because of their mapping properties, they may be expected to have other applications as well.
Download or read book Capacity Theory with Local Rationality written by Robert Rumely and published by American Mathematical Soc.. This book was released on 2013-12-26 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the proof of a deep theorem in arithmetic geometry, the Fekete-Szegö theorem with local rationality conditions. The prototype for the theorem is Raphael Robinson's theorem on totally real algebraic integers in an interval, which says that if is a real interval of length greater than 4, then it contains infinitely many Galois orbits of algebraic integers, while if its length is less than 4, it contains only finitely many. The theorem shows this phenomenon holds on algebraic curves of arbitrary genus over global fields of any characteristic, and is valid for a broad class of sets. The book is a sequel to the author's work Capacity Theory on Algebraic Curves and contains applications to algebraic integers and units, the Mandelbrot set, elliptic curves, Fermat curves, and modular curves. A long chapter is devoted to examples, including methods for computing capacities. Another chapter contains extensions of the theorem, including variants on Berkovich curves. The proof uses both algebraic and analytic methods, and draws on arithmetic and algebraic geometry, potential theory, and approximation theory. It introduces new ideas and tools which may be useful in other settings, including the local action of the Jacobian on a curve, the "universal function" of given degree on a curve, the theory of inner capacities and Green's functions, and the construction of near-extremal approximating functions by means of the canonical distance.
Download or read book Coding Theory and Algebraic Geometry written by Henning Stichtenoth and published by Springer. This book was released on 2006-11-15 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: About ten years ago, V.D. Goppa found a surprising connection between the theory of algebraic curves over a finite field and error-correcting codes. The aim of the meeting "Algebraic Geometry and Coding Theory" was to give a survey on the present state of research in this field and related topics. The proceedings contain research papers on several aspects of the theory, among them: Codes constructed from special curves and from higher-dimensional varieties, Decoding of algebraic geometric codes, Trace codes, Exponen- tial sums, Fast multiplication in finite fields, Asymptotic number of points on algebraic curves, Sphere packings.
Download or read book Existence of the Sectional Capacity written by Robert Rumely and published by American Mathematical Soc.. This book was released on 2000 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the case where the norms are induced by metrics on the fibres of ${\mathcal L}$, we establish the functoriality of the sectional capacity under base change, pullbacks by finite surjective morphisms, and products. We study the continuity of $S Gamma(\overline{\mathcal L})$ under variation of the metric and line bundle, and we apply this to show that the notion of $v$-adic sets in $X(\mathbb C v)$ of capacity $0$ is well-defined. Finally, we show that sectional capacities for arbitrary norms can be well-approximated using objects of finite type.
Download or read book Number Theory written by Canadian Number Theory Association. Conference and published by American Mathematical Soc.. This book was released on 1995 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains proceedings presented at the fourth Canadian Number Theory Association conference held at Dalhousie University in July 1994. The invited speakers focused on analytic, algebraic, and computational number theory. The contributed talks represented a wide variety of areas in number theory.
Download or read book Advances in Complex Analysis and Operator Theory written by Fabrizio Colombo and published by Birkhäuser. This book was released on 2017-09-30 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers contributions written by Daniel Alpay’s friends and collaborators. Several of the papers were presented at the International Conference on Complex Analysis and Operator Theory held in honor of Professor Alpay’s 60th birthday at Chapman University in November 2016. The main topics covered are complex analysis, operator theory and other areas of mathematics close to Alpay’s primary research interests. The book is recommended for mathematicians from the graduate level on, working in various areas of mathematical analysis, operator theory, infinite dimensional analysis, linear systems, and stochastic processes.
Download or read book Arithmetic Geometry written by G. Cornell and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the result of a (mainly) instructional conference on arithmetic geometry, held from July 30 through August 10, 1984 at the University of Connecticut in Storrs. This volume contains expanded versions of almost all the instructional lectures given during the conference. In addition to these expository lectures, this volume contains a translation into English of Falt ings' seminal paper which provided the inspiration for the conference. We thank Professor Faltings for his permission to publish the translation and Edward Shipz who did the translation. We thank all the people who spoke at the Storrs conference, both for helping to make it a successful meeting and enabling us to publish this volume. We would especially like to thank David Rohrlich, who delivered the lectures on height functions (Chapter VI) when the second editor was unavoidably detained. In addition to the editors, Michael Artin and John Tate served on the organizing committee for the conference and much of the success of the conference was due to them-our thanks go to them for their assistance. Finally, the conference was only made possible through generous grants from the Vaughn Foundation and the National Science Foundation.
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first Supplementary volume to Kluwer's highly acclaimed Encyclopaedia of Mathematics. This additional volume contains nearly 600 new entries written by experts and covers developments and topics not included in the already published 10-volume set. These entries have been arranged alphabetically throughout. A detailed index is included in the book. This Supplementary volume enhances the existing 10-volume set. Together, these eleven volumes represent the most authoritative, comprehensive up-to-date Encyclopaedia of Mathematics available.
Download or read book Singularity Theory and its Applications written by David Mond and published by Springer. This book was released on 2006-11-14 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: A workshop on Singularities, Bifurcation and Dynamics was held at Warwick in July 1989 as part of a year-long symposium on Singularity Theory and its applications. The proceedings fall into two halves: Volume I mainly on connections with algebraic geometry and volume II on connections with dynamical systems theory, bifurcation theory, and applications in the sciences. The papers are orginal research, stimulated by the symposium and workshops: All have been refereed, and none will appear elsewhere. The main topic, deformation theory, is represented by several papers on descriptions of the bases of versal deformations, and several more on descriptions of the generic fibres. Other topics include stratifications, and applications to differential geometry.
Download or read book Selected Papers on Analysis Probability and Statistics written by Katsumi Nomizu and published by American Mathematical Soc.. This book was released on 1994 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents papers in the general area of mathematical analysis as it pertains to probability and statistics, dynamical systems, differential equations, and analytic function theory. Among the topics discussed are: stochastic differential equations, spectra of the Laplacian and Schrödinger operators, nonlinear partial differential equations which generate dissipative dynamical systems, fractal analysis on self-similar sets, and the global structure of analytic functions.
Download or read book H Control Theory written by Edoardo Mosca and published by Springer. This book was released on 2006-11-14 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fundamental problem in control engineering is to provide robust performance to uncertain plants. H -control theory began in the early eighties as an attempt to lay down rigorous foundations on the classical robust control requirements. It now turns out that H -control theory is at the crossroads of several important directions of research space or polynomial approach to control and classical interpolation theory; harmonic analysis and operator theory; minimax LQ stochastic control and integral equations. The book presents the underlying fundamental ideas, problems and advances through the pen of leading contributors to the field, for graduate students and researchers in both engineering and mathematics. From the Contents: C. Foias: Commutant Lifting Techniques for Computing Optimal H Controllers.- B.A. Francis: Lectures on H Control and Sampled-Data Systems.- J.W. Helton: Two Topics in Systems Engineering Frequency Domain Design and Nonlinear System.- H. Kwakernaak: The Polynomial Approach to H -Optimal Regulation.- J.B. Pearson: A Short Course in l - Optimal Control
Download or read book Non Archimedean L Functions written by Alexei A. Panchishkin and published by Springer. This book was released on 2013-11-11 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1) p n=1 The set of arguments s for which ((s) is defined can be extended to all s E C,s :f:. 1, and we may regard C as the group of all continuous quasicharacters C = Hom(R~, c>
Download or read book Global Analysis Studies and Applications V written by Yuri G. Borisovich and published by Springer. This book was released on 2006-11-15 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume (a sequel to LNM 1108, 1214, 1334 and 1453) continues the presentation to English speaking readers of the Voronezh University press series on Global Analysis and Its Applications. The papers are selected fromtwo Russian issues entitled "Algebraic questions of Analysis and Topology" and "Nonlinear Operators in Global Analysis". CONTENTS: YuE. Gliklikh: Stochastic analysis, groups of diffeomorphisms and Lagrangian description of viscous incompressible fluid.- A.Ya. Helemskii: From topological homology: algebras with different properties of homological triviality.- V.V. Lychagin, L.V. Zil'bergleit: Duality in stable Spencer cohomologies.- O.R. Musin: On some problems of computational geometry and topology.- V.E. Nazaikinskii, B.Yu. Sternin, V.E.Shatalov: Introduction to Maslov's operational method (non-commutative analysis and differential equations).- Yu.B. Rudyak: The problem of realization of homology classes from Poincare up to the present.- V.G. Zvyagin, N.M. Ratiner: Oriented degree of Fredholm maps of non-negativeindex and its applications to global bifurcation of solutions.- A.A. Bolibruch: Fuchsian systems with reducible monodromy and the Riemann-Hilbert problem.- I.V. Bronstein, A.Ya. Kopanskii: Finitely smooth normal forms of vector fields in the vicinity of a rest point.- B.D. Gel'man: Generalized degree of multi-valued mappings.- G.N. Khimshiashvili: On Fredholmian aspects of linear transmission problems.- A.S. Mishchenko: Stationary solutions of nonlinear stochastic equations.- B.Yu. Sternin, V.E. Shatalov: Continuation of solutions to elliptic equations and localisation of singularities.- V.G. Zvyagin, V.T. Dmitrienko: Properness of nonlinear elliptic differential operators in H|lder spaces.
Download or read book Geometric Aspects of Functional Analysis written by Joram Lindenstrauss and published by Springer. This book was released on 2006-11-14 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: The scope of the Israel seminar in geometric aspects of functional analysis during the academic year 89/90 was particularly wide covering topics as diverse as: Dynamical systems, Quantum chaos, Convex sets in Rn, Harmonic analysis and Banach space theory. The large majority of the papers are original research papers.
Download or read book Hilbert s Tenth Problem Relations with Arithmetic and Algebraic Geometry written by Jan Denef and published by American Mathematical Soc.. This book was released on 2000 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the result of a meeting that took place at the University of Ghent (Belgium) on the relations between Hilbert's tenth problem, arithmetic, and algebraic geometry. Included are written articles detailing the lectures that were given as well as contributed papers on current topics of interest. The following areas are addressed: an historical overview of Hilbert's tenth problem, Hilbert's tenth problem for various rings and fields, model theory and local-global principles, including relations between model theory and algebraic groups and analytic geometry, conjectures in arithmetic geometry and the structure of diophantine sets, for example with Mazur's conjecture, Lang's conjecture, and Bücchi's problem, and results on the complexity of diophantine geometry, highlighting the relation to the theory of computation. The volume allows the reader to learn and compare different approaches (arithmetical, geometrical, topological, model-theoretical, and computational) to the general structural analysis of the set of solutions of polynomial equations. It would make a nice contribution to graduate and advanced graduate courses on logic, algebraic geometry, and number theory
Download or read book p adic Geometry written by Matthew Baker and published by American Mathematical Soc.. This book was released on 2008 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: "In recent decades, p-adic geometry and p-adic cohomology theories have become indispensable tools in number theory, algebraic geometry, and the theory of automorphic representations. The Arizona Winter Schoo1 2007, on which the current book is based, was a unique opportunity to introduce graduate students to this subject." "Following invaluable introductions by John Tate and Vladimir Berkovich, two pioneers of non-archimedean geometry, Brian Conrad's chapter introduces the general theory of Tate's rigid analytic spaces, Raynaud's view of them as the generic fibers of formal schemes, and Berkovich spaces. Samit Dasgupta and Jeremy Teitelbaum discuss the p-adic upper half plane as an example of a rigid analytic space and give applications to number theory (modular forms and the p-adic Langlands program). Matthew Baker offers a detailed discussion of the Berkovich projective line and p-adic potential theory on that and more general Berkovich curves. Finally, Kiran Kedlaya discusses theoretical and computational aspects of p-adic cohomology and the zeta functions of varieties. This book will be a welcome addition to the library of any graduate student and researcher who is interested in learning about the techniques of p-adic geometry."--BOOK JACKET.
Download or read book Geometric Aspects of Dwork Theory written by Alan Adolphson and published by Walter de Gruyter. This book was released on 2008-08-22 with total page 1150 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume book collects the lectures given during the three months cycle of lectures held in Northern Italy between May and July of 2001 to commemorate Professor Bernard Dwork (1923 - 1998). It presents a wide-ranging overview of some of the most active areas of contemporary research in arithmetic algebraic geometry, with special emphasis on the geometric applications of the p-adic analytic techniques originating in Dwork's work, their connection to various recent cohomology theories and to modular forms. The two volumes contain both important new research and illuminating survey articles written by leading experts in the field. The book will provide an indispensable resource for all those wishing to approach the frontiers of research in arithmetic algebraic geometry.
