Number Theory An Introduction Via The Density Of Primes 2nd Edition Benjamin Fine by Benjamin Fine, Gerhard Rosenberger (auth.) 9783319438733, 9783319438757, 3319438735, 3319438751 instant download after payment.

Now in its second edition, this textbook provides an introduction and overview of number theory based on the density and properties of the prime numbers. This unique approach offers both a firm background in the standard material of number theory, as well as an overview of the entire discipline. All of the essential topics are covered, such as the fundamental theorem of arithmetic, theory of congruences, quadratic reciprocity, arithmetic functions, and the distribution of primes. New in this edition are coverage of p-adic numbers, Hensel's lemma, multiple zeta-values, and elliptic curve methods in primality testing.
Key topics and features include:

• A solid introduction to analytic number theory, including full proofs of Dirichlet's Theorem and the Prime Number Theorem
  
• Concise treatment of algebraic number theory, including a complete presentation of primes, prime factorizations in algebraic number fields, and unique factorization of ideals
• Discussion of the AKS algorithm, which shows that primality testing is one of polynomial time, a topic not usually included in such texts
  
• Many interesting ancillary topics, such as primality testing and cryptography, Fermat and Mersenne numbers, and Carmichael numbers