In Search Of The Riemann Zeros

In Search of the Riemann Zeros PDF
Author: Michel Laurent Lapidus
Publisher: American Mathematical Soc.
ISBN: 9780821842225
Size: 77.29 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 558
View: 1907

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In Search Of The Riemann Zeros

by Michel Laurent Lapidus, In Search Of The Riemann Zeros Books available in PDF, EPUB, Mobi Format. Download In Search Of The Riemann Zeros books, Formulated in 1859, the Riemann Hypothesis is the most celebrated and multifaceted open problem in mathematics. In essence, it states that the primes are distributed as harmoniously as possible--or, equivalently, that the Riemann zeros are located on a single vertical line, called the critical line. In this book, the author proposes a new approach to understand and possibly solve the Riemann Hypothesis. His reformulation builds upon earlier (joint) work on complex fractal dimensions and the vibrations of fractal strings, combined with string theory and noncommutative geometry. Accordingly, it relies on the new notion of a fractal membrane or quantized fractal string, along with the modular flow on the associated moduli space of fractal membranes. Conjecturally, under the action of the modular flow, the spacetime geometries become increasingly symmetric and crystal-like, hence, arithmetic. Correspondingly, the zeros of the associated zeta functions eventually condense onto the critical line, towards which they are attracted, thereby explaining why the Riemann Hypothesis must be true. Written with a diverse audience in mind, this unique book is suitable for graduate students, experts and nonexperts alike, with an interest in number theory, analysis, dynamical systems, arithmetic, fractal or noncommutative geometry, and mathematical or theoretical physics.


Horizons Of Fractal Geometry And Complex Dimensions

Horizons of Fractal Geometry and Complex Dimensions PDF
Author: Robert G. Niemeyer
Publisher: American Mathematical Soc.
ISBN: 1470435810
Size: 47.20 MB
Format: PDF, ePub, Docs
Category : Fractals
Languages : en
Pages : 302
View: 5867

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Horizons Of Fractal Geometry And Complex Dimensions

by Robert G. Niemeyer, Horizons Of Fractal Geometry And Complex Dimensions Books available in PDF, EPUB, Mobi Format. Download Horizons Of Fractal Geometry And Complex Dimensions books, This volume contains the proceedings of the 2016 Summer School on Fractal Geometry and Complex Dimensions, in celebration of Michel L. Lapidus's 60th birthday, held from June 21–29, 2016, at California Polytechnic State University, San Luis Obispo, California. The theme of the contributions is fractals and dynamics and content is split into four parts, centered around the following themes: Dimension gaps and the mass transfer principle, fractal strings and complex dimensions, Laplacians on fractal domains and SDEs with fractal noise, and aperiodic order (Delone sets and tilings).


Dr Riemann S Zeros

Dr  Riemann s Zeros PDF
Author: Karl Sabbagh
Publisher: Atlantic Books (UK)
ISBN:
Size: 70.93 MB
Format: PDF, Kindle
Category : Number theory
Languages : en
Pages : 289
View: 3989

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Dr Riemann S Zeros

by Karl Sabbagh, Dr Riemann S Zeros Books available in PDF, EPUB, Mobi Format. Download Dr Riemann S Zeros books, In 1859 Bernhard Riemann, a shy German mathematician, gave an answer to a problem that had long puzzled mathematicians. Although he couldn't provide a proof, Riemann declared that his solution was 'very probably' true. For the next one hundred and fifty years, the world's mathematicians have longed to confirm the Riemann hypothesis. So great is the interest in its solution that in 2001, an American foundation offered a million-dollar prize to the first person to demonstrate that the hypothesis is correct. In this book, Karl Sabbagh makes accessible even the airiest peaks of maths and paints vivid portraits of the people racing to solve the problem. Dr. Riemann's Zeros is a gripping exploration of the mystery at the heart of our counting system.


Analytic Number Theory

Analytic Number Theory PDF
Author: Carl Pomerance
Publisher: Springer
ISBN: 3319222406
Size: 62.86 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 379
View: 3486

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Analytic Number Theory

by Carl Pomerance, Analytic Number Theory Books available in PDF, EPUB, Mobi Format. Download Analytic Number Theory books, This volume contains a collection of research and survey papers written by some of the most eminent mathematicians in the international community and is dedicated to Helmut Maier, whose own research has been groundbreaking and deeply influential to the field. Specific emphasis is given to topics regarding exponential and trigonometric sums and their behavior in short intervals, anatomy of integers and cyclotomic polynomials, small gaps in sequences of sifted prime numbers, oscillation theorems for primes in arithmetic progressions, inequalities related to the distribution of primes in short intervals, the Möbius function, Euler’s totient function, the Riemann zeta function and the Riemann Hypothesis. Graduate students, research mathematicians, as well as computer scientists and engineers who are interested in pure and interdisciplinary research, will find this volume a useful resource. Contributors to this volume: Bill Allombert, Levent Alpoge, Nadine Amersi, Yuri Bilu, Régis de la Bretèche, Christian Elsholtz, John B. Friedlander, Kevin Ford, Daniel A. Goldston, Steven M. Gonek, Andrew Granville, Adam J. Harper, Glyn Harman, D. R. Heath-Brown, Aleksandar Ivić, Geoffrey Iyer, Jerzy Kaczorowski, Daniel M. Kane, Sergei Konyagin, Dimitris Koukoulopoulos, Michel L. Lapidus, Oleg Lazarev, Andrew H. Ledoan, Robert J. Lemke Oliver, Florian Luca, James Maynard, Steven J. Miller, Hugh L. Montgomery, Melvyn B. Nathanson, Ashkan Nikeghbali, Alberto Perelli, Amalia Pizarro-Madariaga, János Pintz, Paul Pollack, Carl Pomerance, Michael Th. Rassias, Maksym Radziwiłł, Joël Rivat, András Sárközy, Jeffrey Shallit, Terence Tao, Gérald Tenenbaum, László Tóth, Tamar Ziegler, Liyang Zhang.


Exploring The Riemann Zeta Function

Exploring the Riemann Zeta Function PDF
Author: Hugh Montgomery
Publisher: Springer
ISBN: 3319599690
Size: 14.15 MB
Format: PDF, Docs
Category : Mathematics
Languages : en
Pages : 298
View: 4656

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Exploring The Riemann Zeta Function

by Hugh Montgomery, Exploring The Riemann Zeta Function Books available in PDF, EPUB, Mobi Format. Download Exploring The Riemann Zeta Function books, 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.


Fractal Geometry And Dynamical Systems In Pure And Applied Mathematics Fractals In Pure Mathematics

Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics  Fractals in pure mathematics PDF
Author: David Carfi
Publisher: American Mathematical Soc.
ISBN: 0821891472
Size: 43.42 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 399
View: 694

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Fractal Geometry And Dynamical Systems In Pure And Applied Mathematics Fractals In Pure Mathematics

by David Carfi, Fractal Geometry And Dynamical Systems In Pure And Applied Mathematics Fractals In Pure Mathematics Books available in PDF, EPUB, Mobi Format. Download Fractal Geometry And Dynamical Systems In Pure And Applied Mathematics Fractals In Pure Mathematics books, This volume contains the proceedings from three conferences: the PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics, held November 8-12, 2011 in Messina, Italy; the AMS Special Session on Fractal Geometry in Pure and Applied Mathematics, in memory of Benoit Mandelbrot, held January 4-7, 2012, in Boston, MA; and the AMS Special Session on Geometry and Analysis on Fractal Spaces, held March 3-4, 2012, in Honolulu, HI. Articles in this volume cover fractal geometry (and some aspects of dynamical systems) in pure mathematics. Also included are articles discussing a variety of connections of fractal geometry with other fields of mathematics, including probability theory, number theory, geometric measure theory, partial differential equations, global analysis on non-smooth spaces, harmonic analysis and spectral geometry. The companion volume (Contemporary Mathematics, Volume 601) focuses on applications of fractal geometry and dynamical systems to other sciences, including physics, engineering, computer science, economics, and finance.


The Math Book

The Math Book PDF
Author: Clifford A. Pickover
Publisher: Sterling Publishing Company, Inc.
ISBN: 9781402757969
Size: 67.47 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 527
View: 480

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The Math Book

by Clifford A. Pickover, The Math Book Books available in PDF, EPUB, Mobi Format. Download The Math Book books, This book covers 250 milestones in mathematical history, beginning millions of years ago with ancient "ant odometers" and moving through time to our modern-day quest for new dimensions.


Prime Obsession

Prime Obsession PDF
Author: John Derbyshire
Publisher: Joseph Henry Press
ISBN: 0309141257
Size: 55.45 MB
Format: PDF, ePub, Mobi
Category : Science
Languages : en
Pages : 446
View: 1056

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Prime Obsession

by John Derbyshire, Prime Obsession Books available in PDF, EPUB, Mobi Format. Download Prime Obsession books, In August 1859 Bernhard Riemann, a little-known 32-year old mathematician, presented a paper to the Berlin Academy titled: "On the Number of Prime Numbers Less Than a Given Quantity." In the middle of that paper, Riemann made an incidental remark â€" a guess, a hypothesis. What he tossed out to the assembled mathematicians that day has proven to be almost cruelly compelling to countless scholars in the ensuing years. Today, after 150 years of careful research and exhaustive study, the question remains. Is the hypothesis true or false? Riemann's basic inquiry, the primary topic of his paper, concerned a straightforward but nevertheless important matter of arithmetic â€" defining a precise formula to track and identify the occurrence of prime numbers. But it is that incidental remark â€" the Riemann Hypothesis â€" that is the truly astonishing legacy of his 1859 paper. Because Riemann was able to see beyond the pattern of the primes to discern traces of something mysterious and mathematically elegant shrouded in the shadows â€" subtle variations in the distribution of those prime numbers. Brilliant for its clarity, astounding for its potential consequences, the Hypothesis took on enormous importance in mathematics. Indeed, the successful solution to this puzzle would herald a revolution in prime number theory. Proving or disproving it became the greatest challenge of the age. It has become clear that the Riemann Hypothesis, whose resolution seems to hang tantalizingly just beyond our grasp, holds the key to a variety of scientific and mathematical investigations. The making and breaking of modern codes, which depend on the properties of the prime numbers, have roots in the Hypothesis. In a series of extraordinary developments during the 1970s, it emerged that even the physics of the atomic nucleus is connected in ways not yet fully understood to this strange conundrum. Hunting down the solution to the Riemann Hypothesis has become an obsession for many â€" the veritable "great white whale" of mathematical research. Yet despite determined efforts by generations of mathematicians, the Riemann Hypothesis defies resolution. Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world. Posited a century and a half ago, the Riemann Hypothesis is an intellectual feast for the cognoscenti and the curious alike. Not just a story of numbers and calculations, Prime Obsession is the engrossing tale of a relentless hunt for an elusive proof â€" and those who have been consumed by it.


Abstracts Of Papers Presented To The American Mathematical Society

Abstracts of Papers Presented to the American Mathematical Society PDF
Author: American Mathematical Society
Publisher:
ISBN:
Size: 56.46 MB
Format: PDF, Kindle
Category : Mathematics
Languages : en
Pages :
View: 3846

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Abstracts Of Papers Presented To The American Mathematical Society

by American Mathematical Society, Abstracts Of Papers Presented To The American Mathematical Society Books available in PDF, EPUB, Mobi Format. Download Abstracts Of Papers Presented To The American Mathematical Society books,


Fractal Geometry Complex Dimensions And Zeta Functions

Fractal Geometry  Complex Dimensions and Zeta Functions PDF
Author: Michel L. Lapidus
Publisher: Springer Science & Business Media
ISBN: 0387352082
Size: 17.17 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 460
View: 2333

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Fractal Geometry Complex Dimensions And Zeta Functions

by Michel L. Lapidus, Fractal Geometry Complex Dimensions And Zeta Functions Books available in PDF, EPUB, Mobi Format. Download Fractal Geometry Complex Dimensions And Zeta Functions books, Number theory, spectral geometry, and fractal geometry are interlinked in this study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary. The Riemann hypothesis is given a natural geometric reformulation in context of vibrating fractal strings, and the book offers explicit formulas extended to apply to the geometric, spectral and dynamic zeta functions associated with a fractal.