Duality in Analytic Number Theory [Paperback]

Deals with analytic number theory; many new results.In this stimulating book, aimed at researchers both established and budding, Peter Elliott demonstrates a method and a motivating philosophy that combine to cohere a large part of analytic number theory. Besides its application, the book also illustrates a way of thinking mathematically: the author weaves historical background into the narrative, variant proofs illustrate obstructions, false steps and the development of insight. It is shown how to formulate theorems as well as how to construct their proofs. Connections with other branches of analysis are illustrated by over 250 exercises, structured in chains about individual topics.In this stimulating book, aimed at researchers both established and budding, Peter Elliott demonstrates a method and a motivating philosophy that combine to cohere a large part of analytic number theory. Besides its application, the book also illustrates a way of thinking mathematically: the author weaves historical background into the narrative, variant proofs illustrate obstructions, false steps and the development of insight. It is shown how to formulate theorems as well as how to construct their proofs. Connections with other branches of analysis are illustrated by over 250 exercises, structured in chains about individual topics.In this stimulating book, Elliott demonstrates a method and a motivating philosophy that combine to cohere a large part of analytic number theory, including the hitherto nebulous study of arithmetic functions. Besides its application, the book also illustrates a way of thinking mathematically: The author weaves historical background into the narrative, while variant proofs illustrate obstructions, false steps and the development of insight in a manner reminiscent of Euler. He demonstrates how to formulate theorems as well as how to construct their proofs. Elementary notions from functional analysis, Fourier analysis, functional equations, and stability in mels