Elementary Methods in Number TheorySpringer Science & Business Media, 11 Ιαν 2008 - 514 σελίδες Elementary Methods in Number Theory begins with "a first course in number theory" for students with no previous knowledge of the subject. The main topics are divisibility, prime numbers, and congruences. There is also an introduction to Fourier analysis on finite abelian groups, and a discussion on the abc conjecture and its consequences in elementary number theory. In the second and third parts of the book, deep results in number theory are proved using only elementary methods. Part II is about multiplicative number theory, and includes two of the most famous results in mathematics: the Erdös-Selberg elementary proof of the prime number theorem, and Dirichlets theorem on primes in arithmetic progressions. Part III is an introduction to three classical topics in additive number theory: Warings problems for polynomials, Liouvilles method to determine the number of representations of an integer as the sum of an even number of squares, and the asymptotics of partition functions. Melvyn B. Nathanson is Professor of Mathematics at the City University of New York (Lehman College and the Graduate Center). He is the author of the two other graduate texts: Additive Number Theory: The Classical Bases and Additive Number Theory: Inverse Problems and the Geometry of Sumsets. |
Περιεχόμενα
| 3 | |
| 14 | |
Congruences | 45 |
Primitive Roots and Quadratic Reciprocity 83 | 82 |
Fourier Analysis on Finite Abelian Groups | 121 |
The abc Conjecture | 171 |
Divisors and Primes in Multiplicative Number | 198 |
Divisor Functions 231 | 230 |
References | 288 |
The Prime Number Theorem | 289 |
Primes in Arithmetic Progressions | 325 |
11 | 355 |
Sums of Sequences of Polynomials | 375 |
Liouvilles Identity 401 | 400 |
| 509 | |
Prime Numbers | 267 |
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
abc conjecture arithmetic function asymptotic density completes the proof Compute denote the number diophantine equation Dirichlet character Dirichlet character modulo distinct primes divides divisible divisor function Eatercises element elementary proof equivalent Euler phi function example Exercise exist integers exists an integer f e L*(G Fermat Find all solutions finite abelian group follows formula Fourier group G group of order Hint homomorphism ideal induction inequality infinitely many primes integer-valued polynomial leading coefficient Lemma Let G lim Sup linear loga logloga nonnegative integers nonzero number of solutions number theory obtain odd prime partition polynomial of degree prime number theorem prime positive integers prime powers primitive root modulo quadratic residue quadratic residue modulo real numbers relatively prime relatively prime positive ring sequence set of integers subgroup of G subset sufficiently large sumset Waring’s problem weighted set Wieferich primes Z/mZ