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Analytic Number Theory presents some of the central topics in number theory in a simple and concise fashion. It covers an amazing amount of material, despite the leisurely pace and emphasis on readability. The author's heartfelt enthusiasm enables readers to see what is magical about the subject. Topics included are: The Partition Function; The Erdös-Fuchs Theorem; Sequences without Arithmetic Professions; The Waring Problem; A "Natural" Proof of the Non-vanishing of L-Series, and a Simple Analytic Proof of the Prime Number Theorem - all presented in a surprisingly elegant and efficient manner with clever examples and interesting problems in each chapter. This text is suitable for a graduate course in analytic number theory.

Mathematics. --- Number theory. --- Number Theory. --- Nombres, Théorie des. --- Waring's problem --- Waring, Problème de --- Number study --- Numbers, Theory of --- Algebra --- Nombres, Théories des --- Waring, Problème de --- Nombres, Théorie des --- Nombres premiers --- Theorie des nombres --- Theorie multiplicative

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Functions of complex variables --- Analytic functions --- Fonctions d'une variable complexe --- Fonctions analytiques --- Complex variables --- Elliptic functions --- Functions of real variables --- Functions, Analytic --- Functions, Monogenic --- Functions, Regular --- Regular functions --- Series, Taylor's --- Analytic functions. --- Functions of complex variables.

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This unusual and lively textbook offers a clear and intuitive approach to the classical and beautiful theory of complex variables. With very little dependence on advanced concepts from several-variable calculus and topology, the text focuses on the authentic complex-variable ideas and techniques. Notable additions to "Complex Analysis, Third Edition," include: • The solution of the cubic equation and Newton’s method for approximating the zeroes of any polynomial; • Expanded treatments of the Schwarz reflection principle and of the mapping properties of analytic functions on closed domains; • An introduction to Schwarz-Christoffel transformations and to Dirichlet series; • A streamlined proof of the prime number theorem, and more. Accessible to students at their early stages of mathematical study, this full first year course in complex analysis offers new and interesting motivations for classical results and introduces related topics stressing motivation and technique. Numerous illustrations, examples, and now 300 exercises, enrich the text. Students who master this textbook will emerge with an excellent grounding in complex analysis, and a solid understanding of its wide applicability.

Analytic functions. --- Electronic books. -- local. --- Functions of complex variables. --- Functions of complex variables --- Analytic functions --- Engineering & Applied Sciences --- Mathematics --- Physical Sciences & Mathematics --- Applied Mathematics --- Calculus --- Functions, Analytic --- Functions, Monogenic --- Functions, Regular --- Regular functions --- Complex variables --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Analysis. --- Series, Taylor's --- Elliptic functions --- Functions of real variables --- Global analysis (Mathematics). --- Analysis, Global (Mathematics) --- Differential topology --- Geometry, Algebraic --- 517.1 Mathematical analysis --- Mathematical analysis

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Approximation theory --- Polynomials --- 517.518.8 --- 519.6 --- 681.3*G12 --- 681.3*G12 Approximation: chebyshev; elementary function; least squares; linear approximation; minimax approximation and algorithms; nonlinear and rational approximation; spline and piecewise polynomial approximation (Numerical analysis) --- Approximation: chebyshev; elementary function; least squares; linear approximation; minimax approximation and algorithms; nonlinear and rational approximation; spline and piecewise polynomial approximation (Numerical analysis) --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Computational mathematics. Numerical analysis. Computer programming --- 517.518.8 Approximation of functions by polynomials and their generalizations --- Approximation of functions by polynomials and their generalizations --- Algebra --- Theory of approximation --- Functional analysis --- Functions --- Chebyshev systems --- Mathematical analysis