Recent Progress On Topics Of Ramanujan Sums And Cotangent Sums Associated With The Riemann Hypothesis
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A01=Helmut Maier
A01=Laszlo Toth
A01=Michael Th Rassias
Author_Helmut Maier
Author_Laszlo Toth
Author_Michael Th Rassias
Category=PBH
Dedekind Sums
Discrete Fourier Transform
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Estermann Zeta Function
Exponential Sums
Menon-Type Identities
Ramanujan Sums
Riemann Hypothesis
Riemann Zeta Function
Trigonometric Sums
Product details
- ISBN 9789811246883
- Publication Date: 10 Feb 2022
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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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 Bretèche 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.
