Irregularities in the Distribution of Prime Numbers, J?nos Pintz; Michael Th. Rassias

Автор: Pintz
Название: Irregularities in the Distribution of Prime Numbers
ISBN: 3319927760 ISBN-13(EAN): 9783319927763
Издательство: Springer
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Цена: 60550.00 T
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Описание: This volume presents research and expository papers highlighting the vibrant and fascinating study of irregularities in the distribution of primes. Written by an international group of experts, contributions present a self-contained yet unified exploration of a rapidly progressing area. Emphasis is given to the research inspired by Maier’s matrix method, which established a newfound understanding of the distribution of primes. Additionally, the book provides an historical overview of a large body of research in analytic number theory and approximation theory. The papers published within are intended as reference tools for graduate students and researchers in mathematics.

Автор: Gabor Halasz; Vera T. Sos
Название: Irregularities of Partitions
ISBN: 3540505822 ISBN-13(EAN): 9783540505822
Издательство: Springer
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Цена: 107130.00 T
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Автор: Dimitris Koukoulopoulos
Название: The Distribution of Prime Numbers
ISBN: 1470447541 ISBN-13(EAN): 9781470447540
Издательство: Mare Nostrum (Eurospan)
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Описание: Prime numbers have fascinated mathematicians since the time of Euclid. This book presents some of our best tools to capture the properties of these fundamental objects, beginning with the most basic notions of asymptotic estimates and arriving at the forefront of mathematical research. Detailed proofs of the recent spectacular advances on small and large gaps between primes are made accessible for the first time in textbook form. Some other highlights include an introduction to probabilistic methods, a detailed study of sieves, and elements of the theory of pretentious multiplicative functions leading to a proof of Linnik's theorem. Throughout, the emphasis has been placed on explaining the main ideas rather than the most general results available. As a result, several methods are presented in terms of concrete examples that simplify technical details, and theorems are stated in a form that facilitates the understanding of their proof at the cost of sacrificing some generality. Each chapter concludes with numerous exercises of various levels of difficulty aimed to exemplify the material, as well as to expose the readers to more advanced topics and point them to further reading sources.