On The Coefficients Of Cyclotomic Polynomials

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On The Coefficients Of Cyclotomic Polynomials
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Author : Gennady Bachman
language : en
Publisher: American Mathematical Soc.
Release Date : 1993
On The Coefficients Of Cyclotomic Polynomials written by Gennady Bachman 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 1993 with Mathematics categories.
Let [italic]a([italic]m, [italic]n) denote the [italic]mth coefficient of the [italic]nth cyclotomic polynomial [capital Greek]Phi[subscript italic]n([italic]z), and let [italic]a([italic]m) = max[subscript italic]n [conditional event/restriction/such that] |[italic]a([italic]m, [italic]n)[conditional event/restriction/such that] |. Our principal result is an asymptotic formula for log [italic]a([italic]m) that improves over a recent estimate of Montgomery and Vaughan.
Around The Unit Circle
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Author : James McKee
language : en
Publisher: Springer Nature
Release Date : 2021-12-08
Around The Unit Circle written by James McKee and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-08 with Mathematics categories.
Mahler measure, a height function for polynomials, is the central theme of this book. It has many interesting properties, obtained by algebraic, analytic and combinatorial methods. It is the subject of several longstanding unsolved questions, such as Lehmer’s Problem (1933) and Boyd’s Conjecture (1981). This book contains a wide range of results on Mahler measure. Some of the results are very recent, such as Dimitrov’s proof of the Schinzel–Zassenhaus Conjecture. Other known results are included with new, streamlined proofs. Robinson’s Conjectures (1965) for cyclotomic integers, and their associated Cassels height function, are also discussed, for the first time in a book. One way to study algebraic integers is to associate them with combinatorial objects, such as integer matrices. In some of these combinatorial settings the analogues of several notorious open problems have been solved, and the book sets out this recent work. Many Mahler measure results are proved for restricted sets of polynomials, such as for totally real polynomials, and reciprocal polynomials of integer symmetric as well as symmetrizable matrices. For reference, the book includes appendices providing necessary background from algebraic number theory, graph theory, and other prerequisites, along with tables of one- and two-variable integer polynomials with small Mahler measure. All theorems are well motivated and presented in an accessible way. Numerous exercises at various levels are given, including some for computer programming. A wide range of stimulating open problems is also included. At the end of each chapter there is a glossary of newly introduced concepts and definitions. Around the Unit Circle is written in a friendly, lucid, enjoyable style, without sacrificing mathematical rigour. It is intended for lecture courses at the graduate level, and will also be a valuable reference for researchers interested in Mahler measure. Essentially self-contained, this textbook should also be accessible to well-prepared upper-level undergraduates.
Some Properties Of The Coefficients Of Cyclotomic Polynomials
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Author : Kau-un Lu
language : en
Publisher:
Release Date : 1968
Some Properties Of The Coefficients Of Cyclotomic Polynomials written by Kau-un Lu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with categories.
Classical Theory Of Arithmetic Functions
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Author : R Sivaramakrishnan
language : en
Publisher: CRC Press
Release Date : 1988-12-19
Classical Theory Of Arithmetic Functions written by R Sivaramakrishnan and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-12-19 with Mathematics categories.
This volume focuses on the classical theory of number-theoretic functions emphasizing algebraic and multiplicative techniques. It contains many structure theorems basic to the study of arithmetic functions, including several previously unpublished proofs. The author is head of the Dept. of Mathemati
New Frontiers In Number Theory And Applications
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Author : Jordi Guàrdia
language : en
Publisher: Springer Nature
Release Date : 2024-05-27
New Frontiers In Number Theory And Applications written by Jordi Guàrdia and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-27 with Mathematics categories.
This contributed volume presents recent advances as well as new directions in number theory and its applications. Algebraic and analytic number theory are the main focus with chapters showing how these areas are rapidly evolving. By gathering authors from over seven countries, readers will gain an international perspective on the current state of research as well as potential avenues to explore. Specific topics covered include: Algebraic Number Theory Elliptic curves and Cryptography Hopf Galois theory Analytic and elementary number theory and applications New Frontiers in Number Theory and Applications will appeal to researchers interested in gaining a global view of current research in number theory.
General Expressions For Certain Coefficients In The Cyclotomic Polynomial Psi X
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Author : Sister Mary Andrea Johnston
language : en
Publisher:
Release Date : 1954
General Expressions For Certain Coefficients In The Cyclotomic Polynomial Psi X written by Sister Mary Andrea Johnston and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1954 with Polynomials categories.
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Author :
language : en
Publisher:
Release Date : 1982
written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with categories.
Analytic Number Theory The Halberstam Festschrift 2
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Author : Bruce C. Berndt
language : en
Publisher: Springer Science & Business Media
Release Date : 1996-05-01
Analytic Number Theory The Halberstam Festschrift 2 written by Bruce C. Berndt 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 1996-05-01 with Mathematics categories.
The second of two volumes presenting papers from an international conference on analytic number theory. The two volumes contain 50 papers, with an emphasis on topics such as sieves, related combinatorial aspects, multiplicative number theory, additive number theory, and Riemann zeta-function.
Galois Theory Through Exercises
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Author : Juliusz Brzeziński
language : en
Publisher: Springer
Release Date : 2018-03-21
Galois Theory Through Exercises written by Juliusz Brzeziński and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-21 with Mathematics categories.
This textbook offers a unique introduction to classical Galois theory through many concrete examples and exercises of varying difficulty (including computer-assisted exercises). In addition to covering standard material, the book explores topics related to classical problems such as Galois’ theorem on solvable groups of polynomial equations of prime degrees, Nagell's proof of non-solvability by radicals of quintic equations, Tschirnhausen's transformations, lunes of Hippocrates, and Galois' resolvents. Topics related to open conjectures are also discussed, including exercises related to the inverse Galois problem and cyclotomic fields. The author presents proofs of theorems, historical comments and useful references alongside the exercises, providing readers with a well-rounded introduction to the subject and a gateway to further reading. A valuable reference and a rich source of exercises with sample solutions, this book will be useful to both students and lecturers. Its original concept makes it particularly suitable for self-study.
The Mathematics Of Paul Erd S I
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Author : Ronald L. Graham
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-08-04
The Mathematics Of Paul Erd S I written by Ronald L. Graham 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 2013-08-04 with Mathematics categories.
This is the most comprehensive survey of the mathematical life of the legendary Paul Erdős (1913-1996), one of the most versatile and prolific mathematicians of our time. For the first time, all the main areas of Erdős' research are covered in a single project. Because of overwhelming response from the mathematical community, the project now occupies over 1000 pages, arranged into two volumes. These volumes contain both high level research articles as well as key articles that survey some of the cornerstones of Erdős' work, each written by a leading world specialist in the field. A special chapter "Early Days", rare photographs, and art related to Erdős complement this striking collection. A unique contribution is the bibliography on Erdős' publications: the most comprehensive ever published. This new edition, dedicated to the 100th anniversary of Paul Erdős' birth, contains updates on many of the articles from the two volumes of the first edition, several new articles from prominent mathematicians, a new introduction, more biographical information about Paul Erdős, and an updated list of publications. The first volume contains the unique chapter "Early Days", which features personal memories of Paul Erdős by a number of his colleagues. The other three chapters cover number theory, random methods, and geometry. All of these chapters are essentially updated, most notably the geometry chapter that covers the recent solution of the problem on the number of distinct distances in finite planar sets, which was the most popular of Erdős' favorite geometry problems.