2013, ISBN: 382bd1523d4391873a4e7eed58968c45

-->The aim of the book is to give a smooth analytic continuation from basic subjects including linear algebra, group theory, Hilbert space theory, etc. to number theory. With plenty of… Meer...

-->The aim of the book is to give a smooth analytic continuation from basic subjects including linear algebra, group theory, Hilbert space theory, etc. to number theory. With plenty of practical examples and worked-out exercises, and the scope ranging from these basic subjects made applicable to number-theoretic settings to advanced number theory, this book can then be read without tears. It will be of immense help to the reader to acquire basic sound skills in number theory and its applications.Number theory used to be described as the queen of mathematics, that is, there is no practical use. However, with the development of computers and the security of internet communications, the importance of number theory has been exponentially increasing daily. The raison d'être of the present book in this situation is that it is extremely reader-friendly while keeping the rigor of serious mathematics and in-depth analysis of practical applications to various subjects including control theory and pseudo-random number generation. The use of operators is prevailing rather abundantly in anticipation of applications to electrical engineering, allowing the reader to master these skills without much difficulty. It also delivers a very smooth bridging between elementary subjects including linear algebra and group theory (and algebraic number theory) for the reader to be well-versed in an efficient and effortless way. One of the main features of the book is that it gives several different approaches to the same topic, helping the reader to gain deeper insight and comprehension. Even just browsing through the materials would be beneficial to the reader.--> Contents: Linear Algebraic Approach to Algebraic Number Theory Group-Theoretic Aspects of Algebraic Number Theory Arithmetic Functions and Stieltjes Integrals Number Theory in the Unit Disc Hilbert Space and Number Theory Control Systems and Number Theory --> --> Readership: Advanced undergraduate students, graduate students and researchers interested in the use of operators through number-theoretic examples, number-theoretic control systems, applications of number theory, etc. --> Keywords:Number Theory;Algebraic Number Theory;Hilbert Space;Automorphic L-functions;Control Theory;Number Theory in the Unit Disc;Stieltjes IntegrationReview: Key Features: Starting from linear algebraic approach to algebraic number theory, we move on to Hilbert space theory which is then used in elucidating automorphic L-functions and control theory and the reader can master the skills without too much difficulty In treating summatory functions in number theory, the Stieltjes integration is included which will clarify and unify many techniques used in practice and the elucidation of Lau's theorem on convolution is highlighted. Also given is the Abel–Tauber theorem which applies to an extreme case of the Selberg–Delange type as well as number theory in the unit disc which treats the limiting behavior of modular forms near the real line as that of radial approach to the unit circle. The same aspect is expounded in control theory Many examples and worked-out exercises will help the reader to master the fundamental skills Since the book gives some different approaches to the same topic and so just browsing through it is beneficial WSPC Electrical Engineering & Telecommunications , AU,DE,ES,FR,GB,UK,IT,MX,US, English Technology & Engineering, World Scientific Publishing Company<

2014, ISBN: 382bd1523d4391873a4e7eed58968c45

This book emphasizes the role of symmetry and presents as many viewpoints as possible of an important phenomenon — the functional equation of the associated zeta-function. It start… Meer...

This book emphasizes the role of symmetry and presents as many viewpoints as possible of an important phenomenon — the functional equation of the associated zeta-function. It starts from the basics before warping into the space of new interest; from the ground state to the excited state. For example, the Euler function is treated in several different places, as the number of generators of a finite cyclic group, as one counting the order of the multiplicative group of reduced residue classes modulo q, and as the order and degree of the Galois group of the cyclotomic field, respectively.One of the important principles of learning is to work with the material many times. This book presents many worked-out examples and exercises to enhance the reader's comprehension on the topics covered in an in-depth manner. This is done in a different setting each time such that the reader will always be challenged. For the keen reader, even browsing the text alone, without solving the exercises, will yield some knowledge and enjoyment.Contents: Elements of Algebra Rudiments of Algebraic Number Theory Arithmetical Functions and Stieltjes Integrals Quadratic Reciprocity Through Duality Around Dirichlet L -Functions Control Systems and Number Theory Readership: Advanced undergraduate students, graduate students and researchers interested in algebra through number-theoretic examples, number-theoretic control systems, etc. WSPC Number Theory 9789814425636, AU,DE,ES,FR,GB,UK,IT,MX,US, English Mathematics, World Scientific Publishing Company<

ISBN: 382bd1523d4391873a4e7eed58968c45

-->, World Scientific Publishing Company