Number Theory from an Analytic Point of View
| Author | : Badih Ghusayni |
| Publisher | : Badih Ghusayni |
| Total Pages | : 200 |
| Release | : 2004 |
| Genre | : Number theory |
| ISBN | : 9789953002828 |
Number Theory From An Analytic Point Of View
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Introduction to Analytic and Probabilistic Number Theory
| Author | : G. Tenenbaum |
| Publisher | : Cambridge University Press |
| Total Pages | : 180 |
| Release | : 1995-06-30 |
| Genre | : Mathematics |
| ISBN | : 9780521412612 |
This is a self-contained introduction to analytic methods in number theory, assuming on the part of the reader only what is typically learned in a standard undergraduate degree course. It offers to students and those beginning research a systematic and consistent account of the subject but will also be a convenient resource and reference for more experienced mathematicians. These aspects are aided by the inclusion at the end of each chapter a section of bibliographic notes and detailed exercises.
A Primer of Analytic Number Theory
| Author | : Jeffrey Stopple |
| Publisher | : Cambridge University Press |
| Total Pages | : 404 |
| Release | : 2003-06-23 |
| Genre | : Mathematics |
| ISBN | : 9780521012539 |
An undergraduate-level 2003 introduction whose only prerequisite is a standard calculus course.
A View from the Top
| Author | : Alex Iosevich |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 154 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : 0821843974 |
Based on a capstone course that the author taught to upper division undergraduate students with the goal to explain and visualize the connections between different areas of mathematics and the way different subject matters flow from one another, this book is suitable for those with a basic knowledge of high school mathematics.
Introduction to Analytic Number Theory
| Author | : Tom M. Apostol |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 352 |
| Release | : 2013-06-29 |
| Genre | : Mathematics |
| ISBN | : 1475755791 |
"This book is the first volume of a two-volume textbook for undergraduates and is indeed the crystallization of a course offered by the author at the California Institute of Technology to undergraduates without any previous knowledge of number theory. For this reason, the book starts with the most elementary properties of the natural integers. Nevertheless, the text succeeds in presenting an enormous amount of material in little more than 300 pages."-—MATHEMATICAL REVIEWS
Introduction to Analytic and Probabilistic Number Theory
| Author | : Gérald Tenenbaum |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 656 |
| Release | : 2015-07-16 |
| Genre | : Mathematics |
| ISBN | : 082189854X |
This book provides a self contained, thorough introduction to the analytic and probabilistic methods of number theory. The prerequisites being reduced to classical contents of undergraduate courses, it offers to students and young researchers a systematic and consistent account on the subject. It is also a convenient tool for professional mathematicians, who may use it for basic references concerning many fundamental topics. Deliberately placing the methods before the results, the book will be of use beyond the particular material addressed directly. Each chapter is complemented with bibliographic notes, useful for descriptions of alternative viewpoints, and detailed exercises, often leading to research problems. This third edition of a text that has become classical offers a renewed and considerably enhanced content, being expanded by more than 50 percent. Important new developments are included, along with original points of view on many essential branches of arithmetic and an accurate perspective on up-to-date bibliography. The author has made important contributions to number theory and his mastery of the material is reflected in the exposition, which is lucid, elegant, and accurate. --Mathematical Reviews
A Course in Analytic Number Theory
| Author | : Marius Overholt |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 394 |
| Release | : 2014-12-30 |
| Genre | : Mathematics |
| ISBN | : 1470417065 |
This book is an introduction to analytic number theory suitable for beginning graduate students. It covers everything one expects in a first course in this field, such as growth of arithmetic functions, existence of primes in arithmetic progressions, and the Prime Number Theorem. But it also covers more challenging topics that might be used in a second course, such as the Siegel-Walfisz theorem, functional equations of L-functions, and the explicit formula of von Mangoldt. For students with an interest in Diophantine analysis, there is a chapter on the Circle Method and Waring's Problem. Those with an interest in algebraic number theory may find the chapter on the analytic theory of number fields of interest, with proofs of the Dirichlet unit theorem, the analytic class number formula, the functional equation of the Dedekind zeta function, and the Prime Ideal Theorem. The exposition is both clear and precise, reflecting careful attention to the needs of the reader. The text includes extensive historical notes, which occur at the ends of the chapters. The exercises range from introductory problems and standard problems in analytic number theory to interesting original problems that will challenge the reader. The author has made an effort to provide clear explanations for the techniques of analysis used. No background in analysis beyond rigorous calculus and a first course in complex function theory is assumed.
Analytic Number Theory
| Author | : Henryk Iwaniec |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 615 |
| Release | : 2021-10-14 |
| Genre | : Education |
| ISBN | : 1470467704 |
Analytic Number Theory distinguishes itself by the variety of tools it uses to establish results. One of the primary attractions of this theory is its vast diversity of concepts and methods. The main goals of this book are to show the scope of the theory, both in classical and modern directions, and to exhibit its wealth and prospects, beautiful theorems, and powerful techniques. The book is written with graduate students in mind, and the authors nicely balance clarity, completeness, and generality. The exercises in each section serve dual purposes, some intended to improve readers' understanding of the subject and others providing additional information. Formal prerequisites for the major part of the book do not go beyond calculus, complex analysis, integration, and Fourier series and integrals. In later chapters automorphic forms become important, with much of the necessary information about them included in two survey chapters.
Abstract analytic number theory
| Author | : Knopfmacher |
| Publisher | : Newnes |
| Total Pages | : 333 |
| Release | : 2009-02-04 |
| Genre | : Technology & Engineering |
| ISBN | : 0444107797 |
North-Holland Mathematical Library, Volume 12: Abstract Analytic Number Theory focuses on the approaches, methodologies, and principles of the abstract analytic number theory. The publication first deals with arithmetical semigroups, arithmetical functions, and enumeration problems. Discussions focus on special functions and additive arithmetical semigroups, enumeration and zeta functions in special cases, infinite sums and products, double series and products, integral domains and arithmetical semigroups, and categories satisfying theorems of the Krull-Schmidt type. The text then ponders on semigroups satisfying Axiom A, asymptotic enumeration and "statistical" properties of arithmetical functions, and abstract prime number theorem. Topics include asymptotic properties of prime-divisor functions, maximum and minimum orders of magnitude of certain functions, asymptotic enumeration in certain categories, distribution functions of prime-independent functions, and approximate average values of special arithmetical functions. The manuscript takes a look at arithmetical formations, additive arithmetical semigroups, and Fourier analysis of arithmetical functions, including Fourier theory of almost even functions, additive abstract prime number theorem, asymptotic average values and densities, and average values of arithmetical functions over a class. The book is a vital reference for researchers interested in the abstract analytic number theory.
Analytic Number Theory For Undergraduates
| Author | : Heng Huat Chan |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 125 |
| Release | : 2009-04-21 |
| Genre | : Mathematics |
| ISBN | : 9814365270 |
This book is written for undergraduates who wish to learn some basic results in analytic number theory. It covers topics such as Bertrand's Postulate, the Prime Number Theorem and Dirichlet's Theorem of primes in arithmetic progression.The materials in this book are based on A Hildebrand's 1991 lectures delivered at the University of Illinois at Urbana-Champaign and the author's course conducted at the National University of Singapore from 2001 to 2008.
