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 Free Download On the Asymptotics to all Orders of the Riemann Zeta Function and of a Two-Parameter Generalization of the Riemann Zeta Function by Athanassios S. Fokas, Jonatan Lenells English | 2022 | ISBN: 1470450984 | 128 Pages | True PDF | 1.06 MB  Free Download An Introduction to Riemann-Finsler Geometry by D. Bao , S.-S. Chern , Z. Shen English | PDF | 2000 | 453 Pages | ISBN : 038798948X | 55.4 MB In Riemannian geometry, measurements are made with both yardsticks and protractors. These tools are represented by a family of inner-products. In Riemann-Finsler geometry (or Finsler geometry for short), one is in principle equipped with only a family of Minkowski norms. So ardsticks are assigned but protractors are not. With such a limited tool kit, it is natural to wonder just how much geometry one can uncover and describe?  Free Download Aspects of Integration; Novel Approaches to the Riemann and Lebesgue Integrals; 1 by Guenther Ronald B. English | 2023 | ISBN: 1032481129 | 159 pages | True PDF | 13.98 MB
 Free Download On the Asymptotics to all Orders of the Riemann Zeta Function and of a Two-Parameter Generalization of the Riemann Zeta Function by Athanassios S. Fokas, Jonatan Lenells English | 2022 | ISBN: 1470450984 | 128 Pages | True PDF | 1.06 MB  Abate, "Holomorphic Dynamics on Hyperbolic Riemann Surfaces " English | ISBN: 3110601052 | 2022 | 400 pages | PDF | 7 MB This completely revised and updated edition of the one variable part of the author's classic older book "Iteration Theory of Holomorphic Maps on Taut Manifolds" presents the theory of holomorphic dynamical systems on hyperbolic Riemann surfaces from the very beginning of the subject up to the most recent developments. It is intended both as a reference book for the experts and as an accessible gateway to this beautiful theory for Master and Ph.D. students. It also contains extensive historical notes and references for further readings.  A Modern View of the Riemann Integral English | 2022 | ISBN: 3031117980 | 155 Pages | PDF EPUB (True) | 10 MB This monograph uncovers the full capabilities of the Riemann integral. Setting aside all notions from Lebesgue's theory, the author embarks on an exploration rooted in Riemann's original viewpoint. On this journey, we encounter new results, numerous historical vignettes, and discover a particular handiness for computations and applications.  Toshiaki TAKIGAMI, 敏明 滝上, "Proof of the Riemann Hypothesis" English | 2021 | ASIN: B09K1WTKXS, B084V1ZBXF | EPUB | pages: 24 | 1.1 mb This is a Proof of the Riemann Hypothesis. This is rewritten on February 22.  English | 2021 | ISBN: 1536194220 | 232 pages | True PDF | 13.21 MB This book is an introductory and comprehensive presentation of the Riemann Hypothesis, one of the most important open questions in math today. It is introductory because it is written in an accessible and detailed format that makes it easy to read and understand. And it is comprehensive because it explains and proves all the mathematical ideas surrounding and leading to the formulation of the hypothesis. Chapter 1 begins by defining the zeta function and exploring some of its properties when the argument is a real number. It proceeds to identify the series' domain of convergence and proves Euler's product formula. Chapter 2 introduces complex numbers and the complex analytic tools necessary to understand the zeta function in complex plane. Chapter 3 extends the domain of the zeta function for the first time by introducing the eta function. Presenting proofs by Sondow, it is shown that zeta can be defined for any complex number whose real part is positive. Next, the functional equation of the zeta function is derived in Chapter 4. This provides a method to extend the definition of zeta to the entirety of the complex plane. Chapter 5 is where the Riemann Hypothesis is properly introduced for the first time. It relates the zeros of the zeta and eta functions which leads to a simple formulation of the hypothesis. Chapters 6 and 7 connect the topics of zeta's zeros and the distribution of prime numbers. Chapter 6 introduces Riemann explicit formula and explains the use of Mobius transform to rewrite the prime counting function in terms of the Riemann prime counting one and it provides a detailed numerical example on how to use the Riemann's formula. Chapter 7 derives the von Mangoldt formula via the residue theorem and elucidates some of its important properties. Certain necessary mathematical tools, such as Fourier analysis and theta and gamma functional equations, are included in the appendices to make the chapters more concise and focused. [center]  Reassessing Riemann's Paper: On the Number of Primes Less Than a Given Magnitude by Walter Dittrich English | PDF | 2021 | 110 Pages | ISBN : 3030610489 | 1.9 MB In this book, the author pays tribute to Bernhard Riemann (1826-1866), a mathematician with revolutionary ideas, whose work on the theory of integration, the Fourier transform, the hypergeometric differential equation, etc. contributed immensely to mathematical physics. The text concentrates in particular on Riemann's only work on prime numbers, including ideas - new at the time - such as analytical continuation into the complex plane and the product formula for entire functions. A detailed analysis of the zeros of the Riemann zeta-function is presented. The impact of Riemann's ideas on regularizing infinite values in field theory is also emphasized.  Jürgen Jost, "Compact Riemann Surfaces Ed 2" English | ISBN: 354043299X | 2002 | 278 pages | DJVU | 3 MB Although Riemann surfaces are a time-honoured field, this book is novel in its broad perspective that systematically explores the connection with other fields of mathematics. It can serve as an introduction to contemporary mathematics as a whole as it develops background material from algebraic topology, differential geometry, the calculus of variations, elliptic PDE, and algebraic geometry. It is unique among textbooks on Riemann surfaces in including an introduction to Teichmüller theory. The analytic approach is likewise new as it is based on the theory of harmonic maps. For this 2nd edition the author has further improved aspects of presentation of various parts of the text. |
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