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Best prime numbers and the riemann hypothesis
1. Prime Numbers and the Riemann Hypothesis
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CAMBRIDGE UNIVERSITY PRESSDescription
Prime numbers are beautiful, mysterious, and beguiling mathematical objects. The mathematician Bernhard Riemann made a celebrated conjecture about primes in 1859, the so-called Riemann Hypothesis, which remains to be one of the most important unsolved problems in mathematics. Through the deep insights of the authors, this book introduces primes and explains the Riemann Hypothesis. Students with minimal mathematical background and scholars alike will enjoy this comprehensive discussion of primes. The first part of the book will inspire the curiosity of a general reader with an accessible explanation of the key ideas. The exposition of these ideas is generously illuminated by computational graphics that exhibit the key concepts and phenomena in enticing detail. Readers with more mathematical experience will then go deeper into the structure of primes and see how the Riemann Hypothesis relates to Fourier analysis using the vocabulary of spectra. Readers with a strong mathematical background will be able to connect these ideas to historical formulations of the Riemann Hypothesis.2. The Secret Harmony of Primes
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The sequence of the primes is something of a mystery in number theory' if not in all of mathematics. Hardly any topic has ever fascinated mathematicians more. Euler once said' "Mathematicians have tried in vain' to this day' to discover some order in the sequence of prime numbers' and we have reason to believe that it is a mystery into which the mind will never penetrate". One key question has always been: Does there exist a single' overarching organisational principle that accounts for why any prime follows another prime as the next largest prime in the prime sequence?
A primary aim of this book is to show that such overarching and comprehensive principles do exist and govern the entire prime sequence. To unlock these secrets of harmony, for the enthusiastic reader, it is not necessary to dive too deep into mathematics' but to unveil structures of organisation from different points of view.
The Secret Harmony of Primes was written in 2012-2015 and represents a collection of the author's work in prime number theory throughout the last decades' woven into a comprehensible storyline.
3. The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics
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Harper PerennialDescription
Inthe tradition of Fermats Enigma and Pi, Marcus du Sautoy tells the illuminating, authoritative, and engagingstory of Bernhard Reimann and the ongoing quest tocapture the holy grail of mathematicsthe formula to predict prime numbers.Oliver Sacks, author of The Man Who Mistook His Wife for a Hat, calls TheMusic of the Primes an amazing book....I could not put it down once Ihad started. Simon Winchester, author of The Professor and the Madman,writes, this fascinating account, decoding the inscrutable language of themathematical priesthood, is written like the purest poetry. Marcus du Sautoy's enthusiasm shines through every line of this hymnto the joy of high intelligence, illuminating as it does so even the darkestcorners of his most arcane universe.4. Study of Analytic Number Theory: Riemann's Hypothesis and Prime Number Theorem with Addendum on Integer Partitions
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This monograph explores several classical issues of modern mathematics, and discusses both the historical and research aspects. The brief historical part is focused on Riemann's zeta function and few related problems. The research part starts from direct formulation of simple proofs of both the prime number theorem and Riemann's hypothesis, two intriguing problems of modern mathematics, which applies the concept of Mertens's function and is based on Apostol's and Littlewood's criterions of equivalence.5. The Humans: A Novel
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Simon SchusterDescription
The bestselling, award-winning author of The Radleys is back with his funniest, most devastating dark comedy yet, a silly, sad, suspenseful, and soulful (Philadelphia Inquirer) novel thats full of heart (Entertainment Weekly).When an extra-terrestrial visitor arrives on Earth, his first impressions of the human species are less than positive. Taking the form of Professor Andrew Martin, a prominent mathematician at Cambridge University, the visitor is eager to complete the gruesome task assigned him and hurry home to his own utopian planet, where everyone is omniscient and immortal.
He is disgusted by the way humans look, what they eat, their capacity for murder and war, and is equally baffled by the concepts of love and family. But as time goes on, he starts to realize there may be more to this strange species than he had thought. Disguised as Martin, he drinks wine, reads poetry, develops an ear for rock music, and a taste for peanut butter. Slowly, unexpectedly, he forges bonds with Martins family. He begins to see hope and beauty in the humans imperfection, and begins to question the very mission that brought him there.
Praised by The New York Times as a novelist of great seriousness and talent, author Matt Haig delivers an unlikely story about human nature and the joy found in the messiness of life on Earth. The Humans is a funny, compulsively readable tale that playfully and movingly explores the ultimate subjectourselves.
6. Imagining Numbers
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Barry Mazur invites lovers of poetry to make a leap into mathematics. Through discussions of the role of the imagination and imagery in both poetry and mathematics, Mazur reviews the writings of the early mathematical explorers and reveals the early bafflement of these Renaissance thinkers faced with imaginary numbers. Then he shows us, step-by-step, how to begin imagining these strange mathematical objects ourselves.
7. The Theory of the Riemann Zeta-Function (Oxford Science Publications)
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Used Book in Good ConditionDescription
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.8. Riemann's Zeta Function
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Bernhard Riemann's eight-page paper entitled "On the Number of Primes Less Than a Given Magnitude" was a landmark publication of 1859 that directly influenced generations of great mathematicians, among them Hadamard, Landau, Hardy, Siegel, Jensen, Bohr, Selberg, Artin, and Hecke. This text, by a noted mathematician and educator, examines and amplifies the paper itself, and traces the developments in theory inspired by it. (An English translation of the original document appears in the Appendix.)
Topics include Riemann's main formula, the prime number theorem, de la Valle Poussin's theorem, numerical analysis of roots by Euler-Maclaurin summation, the Riemann-Siegel formula, largescale computations, Fourier analysis, zeros on the line, the Riemann hypothesis and Farey series, alternative proof of the integral formula, Tauberian theorems, Chebyshev's identity, and other related topics.
This inexpensive edition of Edwards' superb high-level study will be welcomed by students and mathematicians. Mathematically inclined general readers will likewise value this influential classic.