The Theory of the Riemann Zeta-function

Author: Late Savilian Professor of Geometry E C Titchmarsh,Titchmarsh, Edward Charles Titchmarsh,Edward Charles Titchmarsh,D. R. Heath-Brown

Publisher: Oxford University Press

ISBN: 9780198533696

Category: Architecture

Page: 412

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The Riemann zeta-function embodies both additive and multiplicative structures in a single function, making it our most important tool in the study of prime numbers. This volume studies all aspects of the theory, starting from first principles and probing the function's own challenging theory, with the famous and still unsolved "Riemann hypothesis" at its heart. The second edition has been revised to include descriptions of work done in the last forty years and is updated with many additional references; it will provide stimulating reading for postgraduates and workers in analytic number theory and classical analysis.

Exploring the Riemann Zeta Function

190 years from Riemann's Birth

Author: Hugh Montgomery,Ashkan Nikeghbali,Michael Th. Rassias

Publisher: Springer

ISBN: 3319599690

Category: Mathematics

Page: 298

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Exploring the Riemann Zeta Function: 190 years from Riemann's Birth presents a collection of chapters contributed by eminent experts devoted to the Riemann Zeta Function, its generalizations, and their various applications to several scientific disciplines, including Analytic Number Theory, Harmonic Analysis, Complex Analysis, Probability Theory, and related subjects. The book focuses on both old and new results towards the solution of long-standing problems as well as it features some key historical remarks. The purpose of this volume is to present in a unified way broad and deep areas of research in a self-contained manner. It will be particularly useful for graduate courses and seminars as well as it will make an excellent reference tool for graduate students and researchers in Mathematics, Mathematical Physics, Engineering and Cryptography.

Schönheit und Geometrie der Zetafunktion

Beobachtungen und Skizzen

Author: Thomas Kromer

Publisher: BoD – Books on Demand

ISBN: 3842305389

Category: Mathematics

Page: 116

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Die Zeta- und die Etafunktion gehören zu den komplexesten Objekten der Mathematik. In einem strikt geometrischen Ansatz erhalten wir unerwartet schöne Bilder ihres Verlaufs durch die komplexe Zahlenebene, zum Teil verblüffende Zusammenhänge werden in 48 Farbabbildungen illustriert. So können wir nachvollziehen, warum Nullstellen nur für komplexe Zahlen s mit einem Realteil von 0,5 möglich sind. Die Riemannsche Vermutung wird plötzlich plausibel!

The Riemann Hypothesis

A Resource for the Afficionado and Virtuoso Alike

Author: Peter Borwein,Stephen Choi,Brendan Rooney,Andrea Weirathmueller

Publisher: Springer Science & Business Media

ISBN: 0387721258

Category: Mathematics

Page: 533

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The Riemann Hypothesis has become the Holy Grail of mathematics in the century and a half since 1859 when Bernhard Riemann, one of the extraordinary mathematical talents of the 19th century, originally posed the problem. While the problem is notoriously difficult, and complicated even to state carefully, it can be loosely formulated as "the number of integers with an even number of prime factors is the same as the number of integers with an odd number of prime factors." The Hypothesis makes a very precise connection between two seemingly unrelated mathematical objects, namely prime numbers and the zeros of analytic functions. If solved, it would give us profound insight into number theory and, in particular, the nature of prime numbers. This book is an introduction to the theory surrounding the Riemann Hypothesis. Part I serves as a compendium of known results and as a primer for the material presented in the 20 original papers contained in Part II. The original papers place the material into historical context and illustrate the motivations for research on and around the Riemann Hypothesis. Several of these papers focus on computation of the zeta function, while others give proofs of the Prime Number Theorem, since the Prime Number Theorem is so closely connected to the Riemann Hypothesis. The text is suitable for a graduate course or seminar or simply as a reference for anyone interested in this extraordinary conjecture.

Mathematics for the General Reader

Author: E.C. Titchmarsh

Publisher: Courier Dover Publications

ISBN: 0486821188

Category: Mathematics

Page: 192

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"A first-class mathematician's lucid, unhurried account of the science of numbers from arithmetic through the calculus." — James R. Newman, The World of Mathematics. This highly accessible introduction to mathematics is geared toward readers seeking a firm grasp of the essentials of mathematical theory and practice. The treatment also offers a concise outline of mathematical history and a clearer notion of why mathematicians do what they do. Author E. C. Titchmarsh, who served for many years as Savilian Professor of Geometry at Oxford University, begins with counting and the fundamentals of arithmetic. He guides readers through the complexities of algebra, fractions, geometry, irrational numbers, logarithms, infinite series, complex numbers, quadratic equations, trigonometry, functions, and integral and differential calculus. Titchmarsh's graceful, fluid style helps make complicated topics easier to grasp, and his inclusion of numerous examples will prove especially helpful to readers with little or no background in mathematics.

Bulletin

Classe des sciences mathématiques et naturelles. Sciences mathématiques

Author: Srpska akademija nauka i umetnosti

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 8024

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Functions of One Complex Variable I

Author: John B. Conway

Publisher: Springer Science & Business Media

ISBN: 9780387903286

Category: Mathematics

Page: 317

View: 5417

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This book is intended as a textbook for a first course in the theory of functions of one complex variable for students who are mathematically mature enough to understand and execute E - 8 arguments. The actual pre requisites for reading this book are quite minimal; not much more than a stiff course in basic calculus and a few facts about partial derivatives. The topics from advanced calculus that are used (e.g., Leibniz's rule for differ entiating under the integral sign) are proved in detail. Complex Variables is a subject which has something for all mathematicians. In addition to having applications to other parts of analysis, it can rightly claim to be an ancestor of many areas of mathematics (e.g., homotopy theory, manifolds). This view of Complex Analysis as "An Introduction to Mathe matics" has influenced the writing and selection of subject matter for this book. The other guiding principle followed is that all definitions, theorems, etc.

The Mysteries of the Real Prime

Author: M. J. Shai Haran

Publisher: Oxford University Press

ISBN: 9780198508687

Category: Mathematics

Page: 240

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Highly topical and original monograph, introducing the author's work on the Riemann zeta function and its adelic interpretation of interest to a wide range of mathematicians and physicists.

CMFT

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Geometric function theory

Page: N.A

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Computers in mathematical research

based on the proceedings of a conference

Author: Nelson M. Stephens,Institute of Mathematics and Its Applications

Publisher: Oxford University Press, USA

ISBN: N.A

Category: Mathematics

Page: 251

View: 9914

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In this stimulating volume, mathematicians from a wide range of disciplines explore the many ways in which computers are used in research within their fields, both to explore new topics and prove results. There are contributions on the impact of the computer on research in number theory (including the Riemann Zeta function), cryptography, combinatorics, symbolic manipulation, geometry, group theory, statistics, and applied mathematics. Readers will find up-to-date results and uniquely interesting reviews of current work.

Actas

Author: Antonio A. R. Monteiro

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 3493

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