The Development Of Prime Number Theory
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The Development Of Prime Number Theory
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Author : Wladyslaw Narkiewicz
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
The Development Of Prime Number Theory written by Wladyslaw Narkiewicz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
1. People were already interested in prime numbers in ancient times, and the first result concerning the distribution of primes appears in Euclid's Elemen ta, where we find a proof of their infinitude, now regarded as canonical. One feels that Euclid's argument has its place in The Book, often quoted by the late Paul ErdOs, where the ultimate forms of mathematical arguments are preserved. Proofs of most other results on prime number distribution seem to be still far away from their optimal form and the aim of this book is to present the development of methods with which such problems were attacked in the course of time. This is not a historical book since we refrain from giving biographical details of the people who have played a role in this development and we do not discuss the questions concerning why each particular person became in terested in primes, because, usually, exact answers to them are impossible to obtain. Our idea is to present the development of the theory of the distribu tion of prime numbers in the period starting in antiquity and concluding at the end of the first decade of the 20th century. We shall also present some later developments, mostly in short comments, although the reader will find certain exceptions to that rule. The period of the last 80 years was full of new ideas (we mention only the applications of trigonometrical sums or the advent of various sieve methods) and certainly demands a separate book.
The Prime Number Theorem
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Author : G. J. O. Jameson
language : en
Publisher: Cambridge University Press
Release Date : 2003-04-17
The Prime Number Theorem written by G. J. O. Jameson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-17 with Mathematics categories.
At first glance the prime numbers appear to be distributed in a very irregular way amongst the integers, but it is possible to produce a simple formula that tells us (in an approximate but well defined sense) how many primes we can expect to find that are less than any integer we might choose. The prime number theorem tells us what this formula is and it is indisputably one of the great classical theorems of mathematics. This textbook gives an introduction to the prime number theorem suitable for advanced undergraduates and beginning graduate students. The author's aim is to show the reader how the tools of analysis can be used in number theory to attack a 'real' problem, and it is based on his own experiences of teaching this material.
Additive Theory Of Prime Numbers
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Author : Luogeng Hua
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-12-04
Additive Theory Of Prime Numbers written by Luogeng Hua 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 2009-12-04 with Mathematics categories.
Loo-Keng Hua was a master mathematician, best known for his work using analytic methods in number theory. In particular, Hua is remembered for his contributions to Waring's Problem and his estimates of trigonometric sums. Additive Theory of Prime Numbers is an exposition of the classic methods as well as Hua's own techniques, many of which have now also become classic. An essential starting point is Vinogradov's mean-value theorem for trigonometric sums, which Hua usefully rephrases and improves. Hua states a generalized version of the Waring-Goldbach problem and gives asymptotic formulas for the number of solutions in Waring's Problem when the monomial $x^k$ is replaced by an arbitrary polynomial of degree $k$. The book is an excellent entry point for readers interested in additive number theory. It will also be of value to those interested in the development of the now classic methods of the subject.
Number Theory And Its History
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Author : Oystein Ore
language : en
Publisher: Courier Corporation
Release Date : 2012-07-06
Number Theory And Its History written by Oystein Ore and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-06 with Mathematics categories.
Unusually clear, accessible introduction covers counting, properties of numbers, prime numbers, Aliquot parts, Diophantine problems, congruences, much more. Bibliography.
Introduction To Modern Prime Number Theory
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Author : T. Estermann
language : en
Publisher: Cambridge University Press
Release Date : 2011-08-11
Introduction To Modern Prime Number Theory written by T. Estermann and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-11 with Mathematics categories.
This 1952 book attempts to prove the Vinogradov-Goldbach theorem: that every sufficiently large odd number is the sum of three primes.
The Theory Of Numbers
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Author : R. D. Carmichael
language : en
Publisher: Prabhat Prakashan
Release Date : 1914-01-01
The Theory Of Numbers written by R. D. Carmichael and has been published by Prabhat Prakashan this book supported file pdf, txt, epub, kindle and other format this book has been release on 1914-01-01 with Mathematics categories.
Prime Numbers The Holy Grail Of Mathematics
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Author : Thamer Naouech
language : en
Publisher: Thamer Naouech
Release Date : 2020-10-20
Prime Numbers The Holy Grail Of Mathematics written by Thamer Naouech and has been published by Thamer Naouech this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-20 with Juvenile Nonfiction categories.
It is undeniable how prime numbers are one of the most beautiful and fascinating topics in mathematics. But what are prime numbers? Are they only numbers that are divisible by 1 and themselves, or do they have another interesting hidden face?Throughout history, the mystery of prime numbers has challenged the greatest minds in mathematics starting from Euclid of Alexandria to Fermat, Euler, Gauss, and Erdős,… who attempted to solve the puzzling problem of primes. The achievements they realized and the secrets they revealed can only assert how deep the concept of prime numbers is. Starting from how prime numbers exist in nature, and how they are of great use in modern cryptography on which our daily life completely depends, the author travels in the holy kingdom of primes diving into some conjectures involving those special numbers. From the Riemann Hypothesis and the well-known zeta function, he explains how a note in the margin turned to be Fermat’s Last Theorem, one of the most important problems in the history of mathematics. From Mersenne Primes, he gets to the twin primes, those shining little stars in the blue sky of primes. And from Euclid’s proof of the infinite number of primes he gets to a hidden pattern in the distribution of primes discovered by Stanisław Ulam and called the Ulam Spiral. After this little trip, you will know, dear reader, why prime numbers deserve to be called "the holy grail of mathematics".
Number Theory
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Author :
language : en
Publisher: Academic Press
Release Date : 1986-05-05
Number Theory written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-05-05 with Mathematics categories.
This book is written for the student in mathematics. Its goal is to give a view of the theory of numbers, of the problems with which this theory deals, and of the methods that are used. We have avoided that style which gives a systematic development of the apparatus and have used instead a freer style, in which the problems and the methods of solution are closely interwoven. We start from concrete problems in number theory. General theories arise as tools for solving these problems. As a rule, these theories are developed sufficiently far so that the reader can see for himself their strength and beauty, and so that he learns to apply them. Most of the questions that are examined in this book are connected with the theory of diophantine equations - that is, with the theory of the solutions in integers of equations in several variables. However, we also consider questions of other types; for example, we derive the theorem of Dirichlet on prime numbers in arithmetic progressions and investigate the growth of the number of solutions of congruences.
Additive Theory Of Prime Numbers
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Author :
language : en
Publisher:
Release Date : 1966
Additive Theory Of Prime Numbers written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with categories.
Prime Obsession
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Author : John Derbyshire
language : en
Publisher: Joseph Henry Press
Release Date : 2003-04-15
Prime Obsession written by John Derbyshire and has been published by Joseph Henry Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-15 with Science categories.
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.