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Trigonometric Sums and Their Applications 2020 ed. [Mīkstie vāki]

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  • Izdošanas datums: 12-Mar-2021
  • Izdevniecība: Springer Nature Switzerland AG
  • ISBN-10: 303037906X
  • ISBN-13: 9783030379063
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Trigonometric Sums and Their Applications 2020 ed.Palielināt
  • Formāts: Paperback / softback, 311 pages, height x width: 235x155 mm, weight: 498 g, 3 Illustrations, color; 1 Illustrations, black and white; X, 311 p. 4 illus., 3 illus. in color., 1 Paperback / softback
  • Izdošanas datums: 12-Mar-2021
  • Izdevniecība: Springer Nature Switzerland AG
  • ISBN-10: 303037906X
  • ISBN-13: 9783030379063
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9783030379063.html
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.











 
On a Category of Cotangent Sums Related to the Nyman-Beurling Criterion for the Riemann Hypothesis
1(28)
Nikita Derevyanko
Kirill Kovalenko
Maksim Zhukovskii
1 Introduction
1(7)
1.1 Nyman-Beurling Criterion for the Riemann Hypothesis
2(3)
1.2 The Cotangent Sum's Applications to Problems Related to the Riemann Hypothesis
5(3)
2 Central Properties of the Cotangent Sum co
8(7)
2.1 Ellipse
12(3)
3 The Maximum of c0 in Rational Numbers in Short Intervals
15(4)
4 The Function g(x) and Moments of c0
19(5)
5 Dedekind Sums
24(1)
6 Sums Appearing in the Nyman-Beurling Criterion for the Riemann Hypothesis Containing the Mobius Function
25(2)
References
27(2)
Recent Progress in the Study of Polynomials with Constrained Coefficients
29(42)
Tamas Erdelyi
1 Ultraflat Sequences of Unimodular Polynomials
31(5)
2 More Recent Results on Ultraflat Sequences of Unimodular Polynomials
36(2)
3 Flatness of Conjugate-Reciprocal Unimodular Polynomials
38(2)
4 Average Lq Norm of Littlewood Polynomials on the Unit Circle
40(1)
5 Rudin-Shapiro Polynomials
41(2)
6 Mahler Measure and Moments of the Rudin-Shapiro Polynomials
43(1)
7 Lemmas for Theorem 6.1
44(1)
8 Saffari's Conjecture on the Shapiro Polynomials
45(1)
9 Consequences of Saffari's Conjecture
46(3)
10 Open Problems Related to the Rudin-Shapiro Polynomials
49(1)
11 On the Size of the Fekete Polynomials on the Unit Circle
50(3)
12 Unimodular Zeros of Self-Reciprocal Polynomials with Coefficients in a Finite Set
53(7)
13 Bourgain's L1 Problem and Related Results
60(4)
Reference
64(7)
Classes of Nonnegative Sine Polynomials
71(14)
Horst Alzer
Man Kam Kwong
1 Introduction and Statement of Main Results
71(3)
2 Lemmas
74(3)
3 Proof of Theorem 1
77(1)
4 Proof of Theorem 2
78(3)
5 Proof of Theorem 3
81(1)
6 Proof of Theorem 4
82(1)
7 Remarks
82(1)
References
83(2)
Inequalities for Weighted Trigonometric Sums
85(12)
Horst Alzer
Omran Kouba
1 Introduction
85(2)
2 A Technical Lemma
87(4)
3 Main Results
91(4)
References
95(2)
Norm Inequalities for Generalized Laplace Transforms
97(22)
J. C. Kuang
1 Introduction
97(3)
2 Main Results
100(2)
3 Proof of Theorem 3
102(5)
4 The Discrete Versions of the Main Results
107(2)
5 Some Applications
109(8)
References
117(2)
On Marcinkiewicz-Zygmund Inequalities at Hermite Zeros and Their Airy Function Cousins
119(30)
D. S. Lubinsky
1 Introduction
119(10)
2 Proof of Theorems 1.3 and 1.4
129(17)
References
146(3)
The Maximum of Cotangent Sums Related to the Nyman-Beurling Criterion for the Riemann Hypothesis
149(10)
Helmut Maier
Michael Th. Rassias
Andrei Raigorodskii
1 Introduction
150(3)
2 Exponential Sums over Primes in Finite Fields
153(1)
3 Other Preliminary Lemmas
154(3)
4 Proof of Theorem 1.5
157(1)
References
158(1)
Double-Sided Taylor's Approximations and Their Applications in Theory of Trigonometric Inequalities
159(10)
Branko Malesevic
Tatjana Lutovac
Marija Rasajski
Bojan Banjac
1 Introduction
159(1)
2 An Overview of the Results Related to Double-Sided Taylor's Approximations
160(2)
3 Main Results
162(4)
3.1 Generalization of Statement 1
162(2)
3.2 An Improvement of Statement 2
164(2)
4 Conclusion
166(1)
References
166(3)
The Second Moment of the First Derivative of Hardy's Z-Function
169(14)
Maxim A. Korolev
Andrei V. Shubin
1 Introduction
169(2)
2 Auxiliary Lemmas
171(2)
3 Proof of the Main Theorem
173(9)
References
182(1)
Dedekind and Hardy Type Sums and Trigonometric Sums Induced by Quadrature Formulas
183(46)
Gradimir V. Milovanovic
Yilmaz Simsek
1 Introduction and Preliminaries
183(3)
2 Lambert and Eisenstein Series
186(5)
2.1 Further Remarks and Observations for Eisenstein Series
189(2)
3 Dedekind Sums
191(7)
3.1 Some Others Formulas for the Dedekind Sums
196(2)
4 Hardy Sums
198(5)
5 Dedekind Type Daehee-Changhee (DC) Sums
203(2)
6 Trigonometric Representation of the DC-Sums
205(3)
7 DC-Sums Related to Special Functions
208(2)
8 Reciprocity Law
210(6)
9 Sums Obtained from Gauss-Chebyshev Quadratures
216(7)
10 Sums Obtained from Trigonometric Quadrature Rules
223(2)
References
225(4)
On a Half-Discrete Hilbert-Type Inequality in the Whole Plane with the Kernel of Hyperbolic Secant Function Related to the Hurwitz Zeta Function
229(32)
Michael Th. Rassias
Bicheng Yang
Andrei Raigorodskii
1 Introduction
230(2)
2 Weight Functions and Some Lemmas
232(6)
3 Main Results
238(7)
4 Operator Expressions
245(4)
5 Two Kinds of Equivalent Reverse Inequalities
249(8)
6 Conclusions
257(1)
References
258(3)
A Remark on Sets with Small Wiener Norm
261(12)
I.D. Shkredov
1 Introduction
261(2)
2 Definitions
263(2)
3 On the Multiplicative Energy of Sets with Small Wiener Norm
265(4)
4 On the Quantity M+
269(3)
References
272(1)
Order Estimates of Best Orthogonal Trigonometric Approximations of Classes of Infinitely Differentiable Functions
273(16)
Tetiana A. Stepanyuk
1 Introduction
273(3)
2 Best Orthogonal Trigonometric Approximations of the Classes Lψβ,p 1 < p < ∞, in the Metric of Space L∞
276(6)
3 Best Orthogonal Trigonometric Approximations of the Classes Lφβp.1 in the Metric of Space L∞
282(2)
4 Best Orthogonal Trigonometric Approximations of the Classes Lφβp.1 in the Metric of Spaces Ls, 1 < s < ∞
284(2)
References
286(3)
Equivalent Conditions of a Reverse Hilbert-Type Integral Inequality with the Kernel of Hyperbolic Cotangent Function Related to the Riemann Zeta Function
289(18)
Bicheng Yang
1 Introduction
289(3)
2 An Example and Two Lemmas
292(4)
3 Main Results
296(4)
4 Some Corollaries
300(4)
5 Conclusions
304(1)
References
304(3)
Index 307
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 atthe 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.