In Search Of The Riemann Zeros

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In Search Of The Riemann Zeros

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Author : Michel Laurent Lapidus
language : en
Publisher: American Mathematical Soc.
Release Date : 2008

In Search Of The Riemann Zeros written by Michel Laurent Lapidus and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.

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.

Dr Riemann S Zeroes

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Author : Karl Sabbagh
language : en
Publisher:
Release Date : 2002

Dr Riemann S Zeroes written by Karl Sabbagh and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.

Since its inception by Bernard Riemann in 1859, every pure mathematician has longed for a proof for the Riemann hypothesis. Riemann's hypothesis seeks to explain where every single prime number to infinity will occur. This is the story of the quest for the solution.

Dr Riemann S Zeros

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Author : Karl Sabbagh
language : en
Publisher: Atlantic Books (UK)
Release Date : 2003

Dr Riemann S Zeros written by Karl Sabbagh and has been published by Atlantic Books (UK) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Biography & Autobiography categories.

Since its inception by Bernard Riemann in 1859, every pure mathematician has longed for a proof for the Riemann hypothesis. Riemann's hypothesis seeks to explain where every single prime number to infinity will occur. This is the story of the quest for the solution.

Exploring The Riemann Zeta Function

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Author : Hugh Montgomery
language : en
Publisher: Springer
Release Date : 2017-09-11

Exploring The Riemann Zeta Function written by Hugh Montgomery and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-11 with Mathematics categories.

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.

The Feynman Integral And Feynman S Operational Calculus

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Author :
language : en
Publisher: OUP Oxford
Release Date : 2000-03-16

The Feynman Integral And Feynman S Operational Calculus written by and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-03-16 with Mathematics categories.

The aim of this book is to make accessible to mathematicians, physicists and other scientists interested in qunatum theory, the beautiful but mathematically difficult subjects of the Feynman integral and Feynman's operational calculus. Some advantages of the approaches to the Feynman integral which are treated in detail in this book are the following: the existence of the Feynman integral is established for very general potentials in all four cases; under more restrictive but still broad conditions, three of these Feynman integrals agree with one another and with the unitary group from the usual approach to quantum dynamics; these same three Feynman integrals possess pleasant stability properties. Much of the material covered here was previously available only in the research literature, and the book also contains some new results. The background material in mathematics and physics that motivates the study of the Feynman integral and Feynman's operational calculus is discussed, and detailed proofs are provided for the central results.

Stalking The Riemann Hypothesis

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Author : Daniel Nahum Rockmore
language : en
Publisher: Random House
Release Date : 2011-06-08

Stalking The Riemann Hypothesis written by Daniel Nahum Rockmore and has been published by Random House this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-08 with Mathematics categories.

Like a hunter who sees 'a bit of blood' on the trail, that's how Princeton mathematician Peter Sarnak describes the feeling of chasing an idea that seems to have a chance of success. If this is so, then the jungle of abstractions that is mathematics is full of frenzied hunters these days. They are out stalking big game: the resolution of 'The Riemann Hypothesis', seems to be in their sights. The Riemann Hypothesis is about the prime numbers, the fundamental numerical elements. Stated in 1859 by Professor Bernhard Riemann, it proposes a simple law which Riemann believed a 'very likely' explanation for the way in which the primes are distributed among the whole numbers, indivisible stars scattered without end throughout a boundless numerical universe. Just eight years later, at the tender age of thirty-nine Riemann would be dead from tuberculosis, cheated of the opportunity to settle his conjecture. For over a century, the Riemann Hypothesis has stumped the greatest of mathematical minds, but these days frustration has begun to give way to excitement. This unassuming comment is revealing astounding connections among nuclear physics, chaos and number theory, creating a frenzy of intellectual excitement amplified by the recent promise of a one million dollar bounty. The story of the quest to settle the Riemann Hypothesis is one of scientific exploration. It is peopled with solitary hermits and gregarious cheerleaders, cool calculators and wild-eyed visionaries, Nobel Prize-winners and Fields Medalists. To delve into the Riemann Hypothesis is to gain a window into the world of modern mathematics and the nature of mathematics research. Stalking the Riemann Hypothesis will open wide this window so that all may gaze through it in amazement.

Horizons Of Fractal Geometry And Complex Dimensions

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Author : Robert G. Niemeyer
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-06-26

Horizons Of Fractal Geometry And Complex Dimensions written by Robert G. Niemeyer and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-26 with Mathematics categories.

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).

Fractal Geometry And Applications A Jubilee Of Benoit Mandelbrot

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Author : Michel Laurent Lapidus
language : en
Publisher: American Mathematical Soc.
Release Date : 2004

Fractal Geometry And Applications A Jubilee Of Benoit Mandelbrot written by Michel Laurent Lapidus and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.

This volume offers an excellent selection of cutting-edge articles about fractal geometry, covering the great breadth of mathematics and related areas touched by this subject. Included are rich survey articles and fine expository papers. The high-quality contributions to the volume by well-known researchers--including two articles by Mandelbrot--provide a solid cross-section of recent research representing the richness and variety of contemporary advances in and around fractal geometry. In demonstrating the vitality and diversity of the field, this book will motivate further investigation into the many open problems and inspire future research directions. It is suitable for graduate students and researchers interested in fractal geometry and its applications. This is a two-part volume. Part 1 covers analysis, number theory, and dynamical systems; Part 2, multifractals, probability and statistical mechanics, and applications.

Analytic Number Theory

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Author : Carl Pomerance
language : en
Publisher: Springer
Release Date : 2015-11-18

Analytic Number Theory written by Carl Pomerance and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-18 with Mathematics categories.

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.

An Invitation To Fractal Geometry

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Author : Michel L. Lapidus
language : en
Publisher: American Mathematical Society
Release Date : 2024-12-31

An Invitation To Fractal Geometry written by Michel L. Lapidus and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-31 with Mathematics categories.

This book offers a comprehensive exploration of fractal dimensions, self-similarity, and fractal curves. Aimed at undergraduate and graduate students, postdocs, mathematicians, and scientists across disciplines, this text requires minimal prerequisites beyond a solid foundation in undergraduate mathematics. While fractal geometry may seem esoteric, this book demystifies it by providing a thorough introduction to its mathematical underpinnings and applications. Complete proofs are provided for most of the key results, and exercises of different levels of difficulty are proposed throughout the book. Key topics covered include the Hausdorff metric, Hausdorff measure, and fractal dimensions such as Hausdorff and Minkowski dimensions. The text meticulously constructs and analyzes Hausdorff measure, offering readers a deep understanding of its properties. Through emblematic examples like the Cantor set, the Sierpinski gasket, the Koch snowflake curve, and the Weierstrass curve, readers are introduced to self-similar sets and their construction via the iteration of contraction mappings. The book also sets the stage for the advanced theory of complex dimensions and fractal drums by gently introducing it via a variety of classical examples, including well-known fractal curves. By intertwining historical context with rigorous mathematical exposition, this book serves as both a stand-alone resource and a gateway to deeper explorations in fractal geometry.