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General Expressions For Certain Coefficients In The Cyclotomic Polynomial Psi α X Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of General Expressions For Certain Coefficients In The Cyclotomic Polynomial Psi α X book. This book definitely worth reading, it is an incredibly well-written.
Author : Sister Mary Andrea Johnston
Publisher : Unknown
Page : 48 pages
File Size : 43,5 Mb
Release : 1954
Category : Polynomials
ISBN : UOM:39015068336604
Author : Gennady Bachman
Publisher : American Mathematical Society(RI)
Page : 93 pages
File Size : 53,9 Mb
Release : 2014-08-31
Category : MATHEMATICS
ISBN : 1470400871
This book studies the coefficients of cyclotomic polynomials. Let $a(m, n)$ be the $m$th coefficient of the $n$th cyclotomic polynomial $\Phi_n(z)$, and let $a(m)={\rm max _n \vert a(m, n)\vert$. The principal result is an asymptotic formula for ${\rm log a(m)$ that improves a recent estimate of Montgomery and Vaughan. Bachman also gives similar formulae for the logarithms of the one-sided extrema $a (m)={\rm max _na(m, n)$ and $a_*(m)={\rm min _na(m, n)$. In the course of the proof, estimates are obtained for certain exponential sums which are of independent inter
Author : Anonim
Publisher : Unknown
Page : 910 pages
File Size : 43,5 Mb
Release : 1980
Category : Books on microfilm
ISBN : UOM:39015060465716
Author : Joppe W. Bos,Arjen K. Lenstra
Publisher : Cambridge University Press
Page : 281 pages
File Size : 45,8 Mb
Release : 2017-10-12
Category : Mathematics
ISBN : 9781107109353
This book highlights the many ideas and algorithms that Peter L. Montgomery has contributed to computational number theory and cryptography.
Author : Phong Q. Nguyen,Brigitte Vallée
Publisher : Springer Science & Business Media
Page : 503 pages
File Size : 45,7 Mb
Release : 2009-12-02
Category : Computers
ISBN : 9783642022951
The first book to offer a comprehensive view of the LLL algorithm, this text surveys computational aspects of Euclidean lattices and their main applications. It includes many detailed motivations, explanations and examples.
Author : Kai Diethelm
Publisher : Springer
Page : 247 pages
File Size : 50,8 Mb
Release : 2010-08-18
Category : Mathematics
ISBN : 9783642145742
Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations.
Author : Atsuko Miyaji,Tomoaki Mimoto
Publisher : Unknown
Page : 170 pages
File Size : 45,6 Mb
Release : 2020-10-09
Category : Computers
ISBN : 1013277368
This open access book describes the technologies needed to construct a secure big data infrastructure that connects data owners, analytical institutions, and user institutions in a circle of trust. It begins by discussing the most relevant technical issues involved in creating safe and privacy-preserving big data distribution platforms, and especially focuses on cryptographic primitives and privacy-preserving techniques, which are essential prerequisites. The book also covers elliptic curve cryptosystems, which offer compact public key cryptosystems; and LWE-based cryptosystems, which are a type of post-quantum cryptosystem. Since big data distribution platforms require appropriate data handling, the book also describes a privacy-preserving data integration protocol and privacy-preserving classification protocol for secure computation. Furthermore, it introduces an anonymization technique and privacy risk evaluation technique. This book also describes the latest related findings in both the living safety and medical fields. In the living safety field, to prevent injuries occurring in everyday life, it is necessary to analyze injury data, find problems, and implement suitable measures. But most cases don't include enough information for injury prevention because the necessary data is spread across multiple organizations, and data integration is difficult from a security standpoint. This book introduces a system for solving this problem by applying a method for integrating distributed data securely and introduces applications concerning childhood injury at home and school injury. In the medical field, privacy protection and patient consent management are crucial for all research. The book describes a medical test bed for the secure collection and analysis of electronic medical records distributed among various medical institutions. The system promotes big-data analysis of medical data with a cloud infrastructure and includes various security measures developed in our project to avoid privacy violations. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.
Author : Jean-Pierre Tignol
Publisher : World Scientific Publishing Company
Page : 324 pages
File Size : 47,6 Mb
Release : 2015-12-28
Category : Mathematics
ISBN : 9789814704717
The book gives a detailed account of the development of the theory of algebraic equations, from its origins in ancient times to its completion by Galois in the nineteenth century. The appropriate parts of works by Cardano, Lagrange, Vandermonde, Gauss, Abel, and Galois are reviewed and placed in their historical perspective, with the aim of conveying to the reader a sense of the way in which the theory of algebraic equations has evolved and has led to such basic mathematical notions as "group" and "field". A brief discussion of the fundamental theorems of modern Galois theory and complete proofs of the quoted results are provided, and the material is organized in such a way that the more technical details can be skipped by readers who are interested primarily in a broad survey of the theory. In this second edition, the exposition has been improved throughout and the chapter on Galois has been entirely rewritten to better reflect Galois' highly innovative contributions. The text now follows more closely Galois' memoir, resorting as sparsely as possible to anachronistic modern notions such as field extensions. The emerging picture is a surprisingly elementary approach to the solvability of equations by radicals, and yet is unexpectedly close to some of the most recent methods of Galois theory.
Author : Ivan B. Fesenko,S. V. Vostokov
Publisher : American Mathematical Soc.
Page : 362 pages
File Size : 47,6 Mb
Release : 2002-07-17
Category : Mathematics
ISBN : 9780821832592
This book offers a modern exposition of the arithmetical properties of local fields using explicit and constructive tools and methods. It has been ten years since the publication of the first edition, and, according to Mathematical Reviews, 1,000 papers on local fields have been published during that period. This edition incorporates improvements to the first edition, with 60 additional pages reflecting several aspects of the developments in local number theory. The volume consists of four parts: elementary properties of local fields, class field theory for various types of local fields and generalizations, explicit formulas for the Hilbert pairing, and Milnor -groups of fields and of local fields. The first three parts essentially simplify, revise, and update the first edition. The book includes the following recent topics: Fontaine-Wintenberger theory of arithmetically profinite extensions and fields of norms, explicit noncohomological approach to the reciprocity map with a review of all other approaches to local class field theory, Fesenko's -class field theory for local fields with perfect residue field, simplified updated presentation of Vostokov's explicit formulas for the Hilbert norm residue symbol, and Milnor -groups of local fields. Numerous exercises introduce the reader to other important recent results in local number theory, and an extensive bibliography provides a guide to related areas.
Author : Bogdan Grechuk
Publisher : Springer Nature
Page : 437 pages
File Size : 54,6 Mb
Release : 2021-09-21
Category : Mathematics
ISBN : 9783030806279
Landscape of 21st Century Mathematics offers a detailed cross section of contemporary mathematics. Important results of the 21st century are motivated and formulated, providing an overview of recent progress in the discipline. The theorems presented in this book have been selected among recent achievements whose statements can be fully appreciated without extensive background. Grouped by subject, the selected theorems represent all major areas of mathematics: number theory, combinatorics, analysis, algebra, geometry and topology, probability and statistics, algorithms and complexity, and logic and set theory. The presentation is self-contained with context, background and necessary definitions provided for each theorem, all without sacrificing mathematical rigour. Where feasible, brief indications of the main ideas of a proof are given. Rigorous yet accessible, this book presents an array of breathtaking recent advances in mathematics. It is written for everyone with a background in mathematics, from inquisitive university students to mathematicians curious about recent achievements in areas beyond their own.
Author : Bogdan Grechuk
Publisher : Springer
Page : 446 pages
File Size : 50,7 Mb
Release : 2019-06-15
Category : Mathematics
ISBN : 9783030190965
This book consists of short descriptions of 106 mathematical theorems, which belong to the great achievements of 21st century mathematics but require relatively little mathematical background to understand their formulation and appreciate their importance. The selected theorems of this volume, chosen from the famous Annals of Mathematics journal, cover a broad range of topics from across mathematics. Each theorem description is essentially self-contained, can be read independently of the others, and requires as little preliminary knowledge as possible. Although the sections often start with an informal discussion and toy examples, all the necessary definitions are included and each description culminates in the precise formulation of the corresponding theorem. Filling the gap between surveys written for mathematicians and popular mathematics, this book is intended for readers with a keen interest in contemporary mathematics.
Author : James W. Cogdell,Günter Harder,Stephen Kudla,Freydoon Shahidi
Publisher : Springer
Page : 304 pages
File Size : 42,5 Mb
Release : 2018-08-18
Category : Mathematics
ISBN : 9783319955490
This book discusses the mathematical interests of Joachim Schwermer, who throughout his career has focused on the cohomology of arithmetic groups, automorphic forms and the geometry of arithmetic manifolds. To mark his 66th birthday, the editors brought together mathematical experts to offer an overview of the current state of research in these and related areas. The result is this book, with contributions ranging from topology to arithmetic. It probes the relation between cohomology of arithmetic groups and automorphic forms and their L-functions, and spans the range from classical Bianchi groups to the theory of Shimura varieties. It is a valuable reference for both experts in the fields and for graduate students and postdocs wanting to discover where the current frontiers lie.
Author : Carlisle Adams,Jan Camenisch
Publisher : Springer
Page : 459 pages
File Size : 46,6 Mb
Release : 2018-01-12
Category : Computers
ISBN : 9783319725659
This book contains revised selected papers from the 24th International Conference on Selected Areas in Cryptography, SAC 2017, held in Ottawa, ON, Canada in August 2017. The 23 full papers presented in this volume were carefully reviewed and selected from 66 submissions. The focus of the conference was on specific themes in the area of cryptographic system design and analysis such as: Design and analysis of symmetric key cryptosystems Primitives for symmetric key cryptography, including block and stream ciphers, hash functions, and MAC algorithms Efficient implementations of symmetric and public key algorithms
Author : Nicholas M. Katz
Publisher : Princeton University Press
Page : 236 pages
File Size : 41,8 Mb
Release : 1996
Category : Mathematics
ISBN : 0691011184
Riemann introduced the concept of a "local system" on P1-{a finite set of points} nearly 140 years ago. His idea was to study nth order linear differential equations by studying the rank n local systems (of local holomorphic solutions) to which they gave rise. His first application was to study the classical Gauss hypergeometric function, which he did by studying rank-two local systems on P1- {0,1,infinity}. His investigation was successful, largely because any such (irreducible) local system is rigid in the sense that it is globally determined as soon as one knows separately each of its local monodromies. It became clear that luck played a role in Riemann's success: most local systems are not rigid. Yet many classical functions are solutions of differential equations whose local systems are rigid, including both of the standard nth order generalizations of the hypergeometric function, n F n-1's, and the Pochhammer hypergeometric functions. This book is devoted to constructing all (irreducible) rigid local systems on P1-{a finite set of points} and recognizing which collections of independently given local monodromies arise as the local monodromies of irreducible rigid local systems. Although the problems addressed here go back to Riemann, and seem to be problems in complex analysis, their solutions depend essentially on a great deal of very recent arithmetic algebraic geometry, including Grothendieck's etale cohomology theory, Deligne's proof of his far-reaching generalization of the original Weil Conjectures, the theory of perverse sheaves, and Laumon's work on the l-adic Fourier Transform.
Author : Ilker Inam,Engin Büyükaşık
Publisher : Springer
Page : 363 pages
File Size : 54,5 Mb
Release : 2019-04-17
Category : Mathematics
ISBN : 9783030125585
This volume collects lecture notes and research articles from the International Autumn School on Computational Number Theory, which was held at the Izmir Institute of Technology from October 30th to November 3rd, 2017 in Izmir, Turkey. Written by experts in computational number theory, the chapters cover a variety of the most important aspects of the field. By including timely research and survey articles, the text also helps pave a path to future advancements. Topics include: Modular forms L-functions The modular symbols algorithm Diophantine equations Nullstellensatz Eisenstein series Notes from the International Autumn School on Computational Number Theory will offer graduate students an invaluable introduction to computational number theory. In addition, it provides the state-of-the-art of the field, and will thus be of interest to researchers interested in the field as well.