© 2020

Trigonometric Sums and Their Applications

  • Andrei Raigorodskii
  • Michael Th. Rassias

Table of contents

  1. Front Matter
    Pages i-x
  2. Nikita Derevyanko, Kirill Kovalenko, Maksim Zhukovskii
    Pages 1-28
  3. Horst Alzer, Man Kam Kwong
    Pages 71-84
  4. Horst Alzer, Omran Kouba
    Pages 85-96
  5. Helmut Maier, Michael Th. Rassias, Andrei Raigorodskii
    Pages 149-158
  6. Branko Malešević, Tatjana Lutovac, Marija Rašajski, Bojan Banjac
    Pages 159-167
  7. Maxim A. Korolev, Andrei V. Shubin
    Pages 169-182
  8. Gradimir V. Milovanović, Yilmaz Simsek
    Pages 183-228
  9. I. D. Shkredov
    Pages 261-272
  10. Back Matter
    Pages 307-311

About this book


This volume presents in a unified manner both classic as well as modern research results devoted to trigonometric sums. Such sums play an integral role in the formulation and understanding of a broad spectrum of problems which range over surprisingly many and different research areas. Fundamental and new developments are presented to discern solutions to problems across several scientific disciplines. Graduate students and researchers will find within this book numerous examples and a plethora of results related to trigonometric sums through pure and applied research along with open problems and new directions for future research.


Trigonometric Sums approximation theory analytic number theory problem solving applications special functions Trigonometric Series

Editors and affiliations

  • Andrei Raigorodskii
    • 1
  • Michael Th. Rassias
    • 2
  1. 1.Moscow Institute of Physics and Technology, Dolgoprudny, Russia, Moscow state University, Moscow, Russia, Buryat State University, Ulan-Ude, RussiaCaucasus Mathematical Center, Adyghe State UniversityMaykopRussia
  2. 2.Institute of Mathematics, University of Zurich, Zurich, Switzerland, Moscow Institute of Physics and Technology, Dolgoprudny, RussiaInstitute for Advanced Study Program in Interdisciplinary StudiesPrincetonUSA

About the editors

Andrei Raigorodskii is a Federal Professor of Mathematics at the Moscow Institute of Physics and Technology (MIPT) where he is the Director of the Phystech-School of Applied Mathematics and Computer Science, the Head of the Discrete Mathematics Department, the Head of the Laboratory of Advanced Combinatorics and Network Applications, as well as the Head of the Laboratory of Applied Research MIPT-Sberbank. He is also the Head of the Caucasus Mathematical Center. He lectures at MIPT, MSU, HSE and has published about 200 papers and 20 books. He is the Editor-in-Chief of the Moscow Journal of Combinatorics and Number Theory. In 2011, he was awarded the 2011 Russian President's Prize in Science and Innovation for young scientists.

Michael Th. Rassias  is currently a Latsis Foundation Senior Fellow at the University of Zürich, a visiting researcher at the Institute for Advanced Study, Princeton, as well as a visiting Assistant Professor at the Moscow Institute of Physics and Technology. He obtained his PhD in Mathematics from ETH-Zürich in 2014. During the academic year 2014-2015, he was a Postdoctoral researcher at the Department of Mathematics of Princeton University and the Department of Mathematics of ETH-Zürich, conducting research at Princeton. While at Princeton, he prepared with John F. Nash, Jr.  the volume  "Open Problems in Mathematics", Springer, 2016. He has received several awards in mathematical problem-solving competitions, including a Silver medal at the International Mathematical Olympiad of 2003 in Tokyo. He has authored and edited several books with Springer. His current research interests lie in mathematical analysis, analytic number theory, zeta functions, the Riemann Hypothesis, approximation theory, functional equations and analytic inequalities.

Bibliographic information