Recent Progress on Topics of Ramanujan Sums and Cotangent Sums Associated with the Riemann Hypothesis 9789811246883

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Автор: Maier Helmut, Toth Laszlo, Rassias Michael Th
Название: Recent Progress on Topics of Ramanujan Sums and Cotangent Sums Associated with the Riemann Hypothesis
ISBN: 9789811246883
Издательство: World Scientific Publishing
Издательство: World Scientific Publishing Company
Классификация:

Теория чисел

ISBN-10: 9811246882
Обложка/Формат: Hardback
Страницы: 164
Вес: 0.39 кг.
Дата издания: 10.02.2022
Серия: Monographs in number theory
Язык: English
Размер: 158 x 236 x 28
Читательская аудитория: Tertiary education (us: college)
Ключевые слова: Number theory, MATHEMATICS / General,MATHEMATICS / Measurement,MATHEMATICS / Number Theory
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Поставляется из: США
Описание:

In this monograph, we study recent results on some categories of trigonometric/exponential sums along with various of their applications in Mathematical Analysis and Analytic Number Theory. Through the two chapters of this monograph, we wish to highlight the applicability and breadth of techniques of trigonometric/exponential sums in various problems focusing on the interplay of Mathematical Analysis and Analytic Number Theory. We wish to stress the point that the goal is not only to prove the desired results, but also to present a plethora of intermediate Propositions and Corollaries investigating the behaviour of such sums, which can also be applied in completely different problems and settings than the ones treated within this monograph.

In the present work we mainly focus on the applications of trigonometric/exponential sums in the study of Ramanujan sums - which constitute a very classical domain of research in Number Theory - as well as the study of certain cotangent sums with a wide range of applications, especially in the study of Dedekind sums and a facet of the research conducted on the Riemann Hypothesis. For example, in our study of the cotangent sums treated within the second chapter, the methods and techniques employed reveal unexpected connections with independent and very interesting problems investigated in the past by R de la Bretиche and G Tenenbaum on trigonometric series, as well as by S Marmi, P Moussa and J-C Yoccoz on Dynamical Systems.

Overall, a reader who has mastered fundamentals of Mathematical Analysis, as well as having a working knowledge of Classical and Analytic Number Theory, will be able to gradually follow all the parts of the monograph. Therefore, the present monograph will be of interest to advanced undergraduate and graduate students as well as researchers who wish to be informed on the latest developments on the topics treated.

Recent Progress on Topics of Ramanujan Sums and Cotangent Sums Associated with the Riemann Hypothesis, Maier Helmut, Toth Laszlo, Rassias Michael Th