Recent Progress On Topics Of Ramanujan Sums And Cotangent Sums Associated With The Riemann Hypothesis: 10 - Rilegato

Libro 10 di 10: Monographs in Number Theory

Rassias, Michael Th; Maier, Helmut; Toth, Laszlo

 
9789811246883: Recent Progress On Topics Of Ramanujan Sums And Cotangent Sums Associated With The Riemann Hypothesis: 10
Rilegato
ISBN 10: 9811246882 ISBN 13: 9789811246883
Casa editrice: WSPC, 2021

Sinossi

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.

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Editore
WSPC
Data di pubblicazione
2021
Lingua
Inglese
ISBN 10 
9811246882
ISBN 13 
9789811246883
Rilegatura
Copertina rigida
Numero di pagine
164
Contatto del produttore
non disponibile
Persona responsabile
non disponibile