HOME > 상세정보

상세정보

Introduction to the theory of numbers

Introduction to the theory of numbers (15회 대출)

자료유형
단행본
개인저자
Shapiro, Harold N.
서명 / 저자사항
Introduction to the theory of numbers / Harold N. Shapiro.
발행사항
New York :   Wiley,   c1983.  
형태사항
xii, 459 p. : ill. ; 24 cm.
총서사항
Pure and applied mathematics,0079-8185.
ISBN
0471867373 :
일반주기
"A Wiley-Interscience publication."  
서지주기
Includes bibliographical references and index.
일반주제명
Number theory.
000 00877camuuu200265 a 4500
001 000000110584
005 19980706103419.0
008 820623s1983 nyu b 001 0 eng
010 ▼a 82010929 //r922
020 ▼a 0471867373 : ▼c $39.95 (est.)
040 ▼a DLC ▼c DLC
049 1 ▼l 421032815 ▼f 과학 ▼l 421035658 ▼f 과학
050 0 0 ▼a QA241 ▼b .S445 1983
082 0 0 ▼a 512/.7 ▼2 19
090 ▼a 512.7 ▼b S529i
100 1 ▼a Shapiro, Harold N.
245 1 0 ▼a Introduction to the theory of numbers / ▼c Harold N. Shapiro.
260 ▼a New York : ▼b Wiley, ▼c c1983.
300 ▼a xii, 459 p. : ▼b ill. ; ▼c 24 cm.
490 1 ▼a Pure and applied mathematics, ▼x 0079-8185.
500 ▼a "A Wiley-Interscience publication."
504 ▼a Includes bibliographical references and index.
650 0 ▼a Number theory.
830 0 ▼a Pure and applied mathematics (John Wiley & Sons : unnumbered)

No. 소장처 청구기호 등록번호 도서상태 반납예정일 예약 서비스
No. 1 소장처 중앙도서관/서고7층/ 청구기호 512.7 S529i 등록번호 111549920 도서상태 대출가능 반납예정일 예약 서비스 B M
No. 2 소장처 과학도서관/Sci-Info(2층서고)/ 청구기호 512.7 S529i 등록번호 421032815 도서상태 대출가능 반납예정일 예약 서비스 B M
No. 3 소장처 과학도서관/Sci-Info(2층서고)/ 청구기호 512.7 S529i 등록번호 421035658 도서상태 대출가능 반납예정일 예약 서비스 B M
No. 4 소장처 세종학술정보원/과학기술실/ 청구기호 512.7 S529i 등록번호 151027853 도서상태 대출가능 반납예정일 예약 서비스 B M
No. 소장처 청구기호 등록번호 도서상태 반납예정일 예약 서비스
No. 1 소장처 중앙도서관/서고7층/ 청구기호 512.7 S529i 등록번호 111549920 도서상태 대출가능 반납예정일 예약 서비스 B M
No. 소장처 청구기호 등록번호 도서상태 반납예정일 예약 서비스
No. 1 소장처 과학도서관/Sci-Info(2층서고)/ 청구기호 512.7 S529i 등록번호 421032815 도서상태 대출가능 반납예정일 예약 서비스 B M
No. 2 소장처 과학도서관/Sci-Info(2층서고)/ 청구기호 512.7 S529i 등록번호 421035658 도서상태 대출가능 반납예정일 예약 서비스 B M
No. 소장처 청구기호 등록번호 도서상태 반납예정일 예약 서비스
No. 1 소장처 세종학술정보원/과학기술실/ 청구기호 512.7 S529i 등록번호 151027853 도서상태 대출가능 반납예정일 예약 서비스 B M

컨텐츠정보

목차


CONTENTS
1. Divisibility and Other Beginnings = 1
 1.1. The Ring of Integers = 1
 1.2. The Division Algorithm = 4
 1.3. Subsets of Z = 5
 1.4. Greatest Common Divisor and Least Common Multiple = 8
 1.5. An Alternate Approach of Greatest Common Divisor = 14
 1.6. Pythagorean Triplets = 18
 Notes = 21
 References = 21
2. The Unique Factorization Theorem = 22
 2.1. What is the Unique Factorization Theorem? = 22
 2.2. The Prime Divisibility Lemma as a Route to the UFT = 25
 2.3. The Coprime Divisibility Lemma as a Route to the UFT = 26
 2.4. Purely Inductive Proofs of the UFT = 27
 2.5. A Purely Noninductive Proof of the UFT = 28
 2.6. A New View of G.C.D. and L.C.M. = 31
 2.7. Characterizing Subsets of the integers = 32
 2.8. Some Implications for the Primes = 34
 2.9. Valuations : Another Consequence of the UFT = 37
 Notes = 42
 References = 45
3. Arithmetic Functions = 47
 3.1. The Fundamental Arithmetic Functions = 47
 3.2. The Number of Divisors of n = 48
 3.3. The Sum of the Divisors of n = 50
  3.3A. Odd Perfect Numbers = 53
 3.4. Multiplicative Arithmetic Functions = 58
 3.5. The M$$\ddot o$$bius Function = 61
 3.6. Additive Arithmetic Functions = 70
 3.7. The Euler Function = 71
  3.7A. A Property of the Number 30 = 78
 3.8. Averages of Arithmetic Functions = 81
 Notes = 99
 References = 102
4. The Ring of Arithmetic Functions (A Do-It-Yourself Chapter) = 105
 4.1. Rings of Functions and Convolutions = 105
 4.2. Inverses and Units = 107
 4.3. Inversion Formulas = 109
 4.4. The Natural Valuation in % = 109
 4.5. Derivations = 114
 4.6. Formal Transforms. Dirichlet Series, and Generating Functions = 119
 4.7. Units, Primes, and Unique Factorization = 124
 4.8. Removing the Asymmetry = 125
 Notes = 127
 References = 129
5. Congruences = 131
 5.1. Basic Definitions and Properties = 131
 5.2. Introduction to Polynomial Congruences = 141
 5.3. Linear Congruences = 147
  5.3A. Average of the Divisor Function over Arithmetic Progressions = 150
 5.4. The Chinese Remainder Theorem and Simultaneous Congruences = 154
  5.4A. Simultaneous Congruences for Polynomials in Several Variables = 162
 5.5. The General Polynomial Congruence = 169
  5.5A. Average of the Euler Function over Polynomial Sequences = 175
 5.5B. Average of the Divisor Function over Polynomial Sequences = 181
 Notes = 185
 References = 187
6. Structure of the Reduced Residue Classes = 189
 6.1. Reduced Residue Classes as an Abelian Group = 189
  6.1A. Primes of the Form km + 1 = 191
  6.1B. Basic Notions Concerning Finite Groups = 193
  6.1C. Direct Products in Abelian Groups = 198
 6.2. The Structure of R($$2^a$$) = 203
 6.3. The Structure of R($$p^a$$). p an Odd Prime = 206
 6.4. The General Case of R(m) = 213
  6.4A. The Vandiver-Birkhoff Theorem = 217
 6.5. Characters of R(m) = 227
  6.5A. Primitive Characters = 237
 6.6. Power Residues = 239
 Notes = 241
 References = 243
7. Quadratic Congruences = 246
 7.1. The General Quadratic Congruence = 246
 7.2. Quadratic Residues = 250
 7.3. Gauss' Lemma = 254
 7.4. Proof of the Quadratic Reciprocity Law = 257
  7.4A. Gauss Sums and the Quadratic Reciprocity Law = 260
  7.4B. The Least Positive Nonresidue = 265
  7.4C. Application to a Diophantine Equation = 271
 7.5. The Jacobi Symbol = 273
  7.5A. Inductive Proof of the Reciprocity Law = 278
 Notes = 281
 References = 283
8. Counting Problems (A Do-It-Yourself Chapter) = 284
 8.1. Formulation of the Problems = 284
  8.1A. Prime to a Given Integer and in a Given Progression = 287
  8.1B. Sum of Integers Each Prime to a Given Integer = 289
 8.2. Powerfree Integers = 290
  8.2A. Squarefree Integers in Small Intervals = 294
 8.3. Powerful Integers = 295
 8.4. Power Residues Modulo a Prime = 298
 8.5. Primitive Roots of a Prime = 301
  8.5A. Squareful Primitive Roots = 306
  8.5B. Consecutive Primitive Roots = 308
 8.6. Combinatorial Identities = 312
 Notes = 314
 References = 315
9. The Elements of Prime Number Theory = 317
 9.1. Simple Beginnings = 317
  9.1A. Indirect Counting = 322
 9.2. The Processing of log [x]1 = 327
  9.2A. Bounds and Upper and Lower Limits = 336
  9.2B. A Lower Bound Property of the Eulcr Function = 339
  9.2C. The Number of Prime Factors of an Integer = 341
  9.2D. The Smallest Positive Quadratic Nonresidue = 348
 9.3. Bertrand's Postulate, the Ideas of Chebychev = 350
  9.3A. Proof of Bertrand's Postulate = 357
  9.3B. Ramanujan's Idea = 361
  9.3C. The Erdos Ideas = 363
  9.3D. The Theorem of I Schur = 369
 9.4. Primes in Arithmetic Progressions = 374
  9.4A. A Chebychev Approach to Primes in Arithmetic Progressions = 386
 Notes = 396
 References = 398
10. The Prime Number Theorem = 400
 10.1 Statements of the Prime Number Theorem = 400
 10.2. The Role of the M$$\ddot o$$bius Inversion Formula = 405
 10.3. Equivalent Formulations of the Prime Number Theorem = 408
 10.4. The Selberg Symmetry Formula = 416
 10.5. Immediate Consequences of the Symmetry Formula = 424
 10.6. Selberg's Derivation of the Prime Number Theorem = 428
 10.7. The Erdos Derivation of the Prime Number Theorem = 439
 Notes = 449
 References = 451
Index = 453