Trigonometric Sums and Their Applications

1. Front Matter

   Pages i-x

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2. On a Category of Cotangent Sums Related to the Nyman-Beurling Criterion for the Riemann Hypothesis

   • Nikita Derevyanko, Kirill Kovalenko, Maksim Zhukovskii

   Pages 1-28

3. Recent Progress in the Study of Polynomials with Constrained Coefficients

   • Tamás Erdélyi

   Pages 29-69

4. Classes of Nonnegative Sine Polynomials

   • Horst Alzer, Man Kam Kwong

   Pages 71-84

5. Inequalities for Weighted Trigonometric Sums

   • Horst Alzer, Omran Kouba

   Pages 85-96

6. Norm Inequalities for Generalized Laplace Transforms

   • J. C. Kuang

   Pages 97-117

7. On Marcinkiewicz-Zygmund Inequalities at Hermite Zeros and Their Airy Function Cousins

   • D. S. Lubinsky

   Pages 119-147

8. The Maximum of Cotangent Sums Related to the Nyman-Beurling Criterion for the Riemann Hypothesis

   • Helmut Maier, Michael Th. Rassias, Andrei Raigorodskii

   Pages 149-158

9. Double-Sided Taylor’s Approximations and Their Applications in Theory of Trigonometric Inequalities

   • Branko Malešević, Tatjana Lutovac, Marija Rašajski, Bojan Banjac

   Pages 159-167

10. The Second Moment of the First Derivative of Hardy’s Z-Function

    • Maxim A. Korolev, Andrei V. Shubin

    Pages 169-182

11. Dedekind and Hardy Type Sums and Trigonometric Sums Induced by Quadrature Formulas

    • Gradimir V. Milovanović, Yilmaz Simsek

    Pages 183-228

12. On a Half-Discrete Hilbert-Type Inequality in the Whole Plane with the Kernel of Hyperbolic Secant Function Related to the Hurwitz Zeta Function

    • Michael Th. Rassias, Bicheng Yang, Andrei Raigorodskii

    Pages 229-259

13. A Remark on Sets with Small Wiener Norm

    • I. D. Shkredov

    Pages 261-272

14. Order Estimates of Best Orthogonal Trigonometric Approximations of Classes of Infinitely Differentiable Functions

    • Tetiana A. Stepanyuk

    Pages 273-287

15. Equivalent Conditions of a Reverse Hilbert-Type Integral Inequality with the Kernel of Hyperbolic Cotangent Function Related to the Riemann Zeta Function

    • Bicheng Yang

    Pages 289-305

16. Back Matter

    Pages 307-311

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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

• Moscow Institute of Physics and Technology, Dolgoprudny, Russia, Moscow state University, Moscow, Russia, Buryat State University, Ulan-Ude, Russia, Caucasus Mathematical Center, Adyghe State University, Maykop, Russia

  Andrei Raigorodskii

• Institute of Mathematics, University of Zurich, Zurich, Switzerland, Moscow Institute of Physics and Technology, Dolgoprudny, Russia, Institute for Advanced Study Program in Interdisciplinary Studies, Princeton, USA

  Michael Th. Rassias

​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.

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