Density Of Prime Divisors Of Linear Recurrences
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Density Of Prime Divisors Of Linear Recurrences
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Author : Christian Ballot
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
Density Of Prime Divisors Of Linear Recurrences written by Christian Ballot 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 1995 with Mathematics categories.
A general density theory of the set of prime divisors of a certain family of linear recurring sequences with constant coefficients, a family which is defined for any order recursion, is built up from the work of Lucas, Laxton, Hasse, and Lagarias. In particular, in this theory the notion of the rank of a prime divisor as well as the notion of a Companion Lucas sequence (Lucas), the group associated with a given second-order recursion (Laxton), and the effective computation of densities (Hasse and Lagarias) are first combined and then generalized to any order recursion.
Density Of Prime Divisors Of Linear Recurrences
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Author : Christian Ballot
language : en
Publisher:
Release Date : 1995
Density Of Prime Divisors Of Linear Recurrences written by Christian Ballot and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Divisor theory categories.
Recurrence Sequences
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Author : Graham Everest
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-09-03
Recurrence Sequences written by Graham Everest 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 2015-09-03 with Mathematics categories.
Recurrence sequences are of great intrinsic interest and have been a central part of number theory for many years. Moreover, these sequences appear almost everywhere in mathematics and computer science. This book surveys the modern theory of linear recurrence sequences and their generalizations. Particular emphasis is placed on the dramatic impact that sophisticated methods from Diophantine analysis and transcendence theory have had on the subject. Related work on bilinear recurrences and an emerging connection between recurrences and graph theory are covered. Applications and links to other areas of mathematics are described, including combinatorics, dynamical systems and cryptography, and computer science. The book is suitable for researchers interested in number theory, combinatorics, and graph theory.
The Lucas Sequences
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Author : Christian J.-C. Ballot
language : en
Publisher: Springer Nature
Release Date : 2023-10-19
The Lucas Sequences written by Christian J.-C. Ballot and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-19 with Mathematics categories.
Although the Lucas sequences were known to earlier investigators such as Lagrange, Legendre and Genocchi, it is because of the enormous number and variety of results involving them, revealed by Édouard Lucas between 1876 and 1880, that they are now named after him. Since Lucas’ early work, much more has been discovered concerning these remarkable mathematical objects, and the objective of this book is to provide a much more thorough discussion of them than is available in existing monographs. In order to do this a large variety of results, currently scattered throughout the literature, are brought together. Various sections are devoted to the intrinsic arithmetic properties of these sequences, primality testing, the Lucasnomials, some associated density problems and Lucas’ problem of finding a suitable generalization of them. Furthermore, their application, not only to primality testing, but also to integer factoring, efficient solution of quadratic and cubic congruences, cryptography and Diophantine equations are briefly discussed. Also, many historical remarks are sprinkled throughout the book, and a biography of Lucas is included as an appendix.Much of the book is not intended to be overly detailed. Rather, the objective is to provide a good, elementary and clear explanation of the subject matter without too much ancillary material. Most chapters, with the exception of the second and the fourth, will address a particular theme, provide enough information for the reader to get a feel for the subject and supply references to more comprehensive results. Most of this work should be accessible to anyone with a basic knowledge of elementary number theory and abstract algebra. The book’s intended audience is number theorists, both professional and amateur, students and enthusiasts.
Rational Number Theory In The 20th Century
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Author : Władysław Narkiewicz
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-09-02
Rational Number Theory In The 20th Century written by Władysław Narkiewicz 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 2011-09-02 with Mathematics categories.
The last one hundred years have seen many important achievements in the classical part of number theory. After the proof of the Prime Number Theorem in 1896, a quick development of analytical tools led to the invention of various new methods, like Brun's sieve method and the circle method of Hardy, Littlewood and Ramanujan; developments in topics such as prime and additive number theory, and the solution of Fermat’s problem. Rational Number Theory in the 20th Century: From PNT to FLT offers a short survey of 20th century developments in classical number theory, documenting between the proof of the Prime Number Theorem and the proof of Fermat's Last Theorem. The focus lays upon the part of number theory that deals with properties of integers and rational numbers. Chapters are divided into five time periods, which are then further divided into subject areas. With the introduction of each new topic, developments are followed through to the present day. This book will appeal to graduate researchers and student in number theory, however the presentation of main results without technicalities will make this accessible to anyone with an interest in the area.
Algebraic And Analytic Geometry Of Fans
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Author : Carlos Andradas
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
Algebraic And Analytic Geometry Of Fans written by Carlos Andradas 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 1995 with Mathematics categories.
A set which can be defined by systems of polynomial inequalities is called semialgebraic. When such a description is possible locally around every point, by means of analytic inequalities varying with the point, the set is called semianalytic. If one single system of strict inequalities is enough, either globally or locally at every point, the set is called basic. The topic of this work is the relationship between these two notions. Namely, Andradas and Ruiz describe and characterize, both algebraically and geometrically, the obstructions for a basic semianalytic set to be basic semialgebraic. Then they describe a special family of obstructions that suffices to recognize whether or not a basic semianalytic set is basic semialgebraic. Finally, they use the preceding results to discuss the effect on basicness of birational transformations.
Classification Of Simple C Algebras Inductive Limits Of Matrix Algebras Over Trees
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Author : Liangqing Li
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Classification Of Simple C Algebras Inductive Limits Of Matrix Algebras Over Trees written by Liangqing Li 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 1997 with Mathematics categories.
In this paper, it is shown that the simple unital C*-algebras arising as inductive limits of sequences of finite direct sums of matrix algebras over [italic capital]C([italic capital]X[subscript italic]i), where [italic capital]X[subscript italic]i are arbitrary variable trees, are classified by K-theoretical and tracial data. This result generalizes the result of George Elliott of the case of [italic capital]X[subscript italic]i = [0, 1]. The added generality is useful in the classification of more general inductive limit C*-algebras.
The Index Theorem For Minimal Surfaces Of Higher Genus
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Author : Friedrich Tomi
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
The Index Theorem For Minimal Surfaces Of Higher Genus written by Friedrich Tomi 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 1995 with Mathematics categories.
In this paper we formulate and prove an index theorem for minimal surfaces of higher topological type spanning one boundary contour. Our techniques carry over to surfaces with several boundary contours as well as to unoriented surfaces.
M Kdv Solitons On The Background Of Quasi Periodic Finite Gap Solutions
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Author : Fritz Gesztesy
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
M Kdv Solitons On The Background Of Quasi Periodic Finite Gap Solutions written by Fritz Gesztesy 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 1995 with Mathematics categories.
In the introductory section, we review the formulation of the Korteweg-de Vries (KdV) equation and of the modified KdV (mKdV) equation as a compatibility condition for a Lax pair of linear operators. We then illustrate Miura's transformation, which maps solutions of the mKdV into solutions of the KdV. We then give a general overview of the concept of soliton solutions relative to general backgrounds, and of the single and double commutation methods. Finally, we present the main results of the article. To avoid the clutter of too many technical details, the paper is organized in four sections and five appendices.
Intersection Pairings On Conley Indices
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Author : Henry L. Kurland
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
Intersection Pairings On Conley Indices written by Henry L. Kurland 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 1996 with Mathematics categories.
This memoir is a careful and detailed study of the intersection pairing in the Conley index. The Conley index associates to an isolated invariant set of a semiflow (with some mild compactness conditions) a homotopy type of a space, constructed to be invariant under perturbations of the flow. The homology of this space is the homology Conley index. For a (two-sided) flow, each isolated invariant set has two indices defined: one for the forward flow, and one for the reverse. In general, there is no relationship between these two indices, but when the flow is on an orientable manifold, the two indices can be related by an intersection pairing. It is this pairing that receives a careful and detailed study in this memoir. Results are then applied to the motivating example of the work: the existence of transition layer behavior for two-point boundary value problems of singularly perturbed systems.