This book presents the development of Prime Number Theory from its beginnings until the end of the first decade of the XXth century. Special emphasis is given to the work of Cebysev, Dirichlet, Riemann, Vallée-Poussin, Hadamard and Landau. The book presents the principal results with proofs and also gives, mostly in short comments, an overview of the development in the last 80 years. It is, however, not a historical book since it does not give biographical details of the people who have played a role in the development of Prime Number Theory. The book contains a large list of references with more than 1800 items. It can be read by any person with a knowledge of fundamental notions of number theory and complex analysis.
The Development of Prime Number Theory
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Inside This Book
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First Sentence:
1. The distinction between prime and composite integers as well as the notions of the greatest common divisor and least common multiple already appear in the seventh book of Euclid's1 Elementa (Euclid 300 B.C.). Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
prime number formula, many primes congruent, numeri primi, des nombres premiers, greatest prime factor, difference between consecutive primes, prime number theorem, prime number theory, concerning prime numbers, sur les nombres premiers, sign infinitely, character mod, density hypothesis, prime congruent, prime difference, assertion results, divisor problem, critical strip, tauberian theorem, twin primes, zeta function, infinitely many primes, partial summation, elementary proof, prime values Key Phrases - Capitalized Phrases (CAPs): (learn more)
Prime Number Theorem, Riemann's Hypothesis, Dirichlet's L-functions, Costa Pereira, Goldbach's Conjecture, Wang Yuan, Chen Jing Run, Sankt Petersburg, Cebysev's Theorem, Hadamard's First Paper, Jia Chaohua, Koch's Theorem, The Conjecture of Legendre New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
1. The distinction between prime and composite integers as well as the notions of the greatest common divisor and least common multiple already appear in the seventh book of Euclid's1 Elementa (Euclid 300 B.C.). Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
prime number formula, many primes congruent, numeri primi, des nombres premiers, greatest prime factor, difference between consecutive primes, prime number theorem, prime number theory, concerning prime numbers, sur les nombres premiers, sign infinitely, character mod, density hypothesis, prime congruent, prime difference, assertion results, divisor problem, critical strip, tauberian theorem, twin primes, zeta function, infinitely many primes, partial summation, elementary proof, prime values Key Phrases - Capitalized Phrases (CAPs): (learn more)
Prime Number Theorem, Riemann's Hypothesis, Dirichlet's L-functions, Costa Pereira, Goldbach's Conjecture, Wang Yuan, Chen Jing Run, Sankt Petersburg, Cebysev's Theorem, Hadamard's First Paper, Jia Chaohua, Koch's Theorem, The Conjecture of Legendre New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 46
books:
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- Number Theory by Wladyslaw Narkiewicz on 4 pages
- Collected Papers Vol 2 by Atle Selberg on 4 pages
- The Distribution of Prime Numbers (Cambridge Mathematical Library) by A. E. Ingham in Front Matter, and Back Matter
- Collected Papers (German, English and French Edition) by E. Artin in Back Matter
- Disquisitiones Arithmeticae by Carl F. Gauss in Back Matter
See all 46 books this book cites
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