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Nathanson M.B. — Elementary methods in number theory
Nathanson M.B. — Elementary methods in number theory

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Название: Elementary methods in number theory

Автор: Nathanson M.B.

Аннотация:

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.


Язык: en

Рубрика: Математика/Теория чисел/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 516

Добавлена в каталог: 05.06.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
abc conjecture      185
Abelian group      10
Abelian theorem      486
Abundant number      241 260
Abundant number, k-abundant      260
Abundant number, primitive      260
Additive basis      359
Additive character      325
Additive set function      133
Algebraically closed field      177
Aliquot sequence      243
Arithmetic function      57 201
Asymptotic basis      359
Asymptotic density      244 257 360 475
Asymptotic density, lower      256 482
Asymptotic density, upper      256 482
Asymptotically stable basis      360
Basis      359
Basis of finite order      359
Basis of order h      359
Basis, asymptotic      359
Basis, asymptotically stable      360
Basis, stable      359
Binary operation      10
Binary quadratic form      108 405
Binomial coefficient      8 268
Binomial polynomial      357
Carmichael number      76
Catalan conjecture      186
Catalan equation      184 186
Catalan — Dickson problem      244
Cauchy — Schwarz inequality      139
Ceiling function      xi
CHARACTER      126
Character group      127
Character table      131
Character, additive character      325
Character, complex character      326
Character, Dirichlet character      326
Character, even character      326
Character, induced      328
Character, multiplicative character      326
Character, odd character      326
Character, primitive      328
Character, principal character      326
Character, real character      326
Chebyshev functions      267
Chebyshev's theorem      271
Ciphertext      76
Classical Gauss sum      153
Cofinite      476
Common divisor      12
Common multiple      28
Commutative group      10
Commutative ring      48
Comparative prime number theory      351
Complete set of residues      46
Completely additive      27
Completely multiplicative      226
Complex character      326
Composite number      25
Congruence abc conjecture      191
Congruence class      46
Congruent      45
Congruent polynomials      90
Conjugate divisor      25 405
Continued fraction      19
Convergent      23
Convolution      139
Coset      69
Counting function      256 359 475
Cryptanalysis      77
Cryptography      76
Cusp form      453
Cyclic group      70
Deficient number      241
Degree of polynomial      84
density      256 475
Density, asymptotic      360
Density, Shnirel'man      359
Derivation      175 203
Derivative      116
Diagonalizable operator      146
Difference operator      357
Difference set      361
Diophantine equation      37
Direct product of groups      124
Direct sum      121
Dirichlet character      325 326
Dirichlet convolution      201
Dirichlet L-function      330
Dirichlet polynomial      337
Dirichlet series      337
Dirichlet's divisor problem      233
Dirichlet's theorem      347
Discrete logarithm      88
Discriminant      108
Division algorithm      3
Divisor      3
Divisor function      231 405 431
Double coset      73
Double dual      129
Dual group      127
Eigenvalue      146
Eigenvector      146
Eisenstein series      453
Equivalent polynomials      73
Euclid's lemma      26
Euclid's theorem      33
Euclidean algorithm      18
Euclidean algorithm, length      18
Euler phi function      54 57 227
Euler product      330
Euler's constant      213
Euler's theorem      67
Evaluation map      85
Even character      326
Even function      401
Eventually coincide      397
Exactly divide      27
EXPONENT      83
Exponential congruence      97
Factorization      234
Fermat prime      36 107
Fermat's last theorem      183 185
Fermat's little theorem      68
Fermat's theorem      407
Fibonacci numbers      23
Field      49
Floor function      xi
Formal power series      205
Fourier transform      135 160
Fractional part      29 206
Frobenius problem      39
Fundamental Theorem of Arithmetic      26
Gauss sum      152
Gauss sum, classical      153
Gauss's lemma      103
Gaussian integer      453
Gaussian set      103
Generalized von Mangoldt function      290
Generating function      483
Generator      70
Greatest common divisor      12
Greatest common divisor, polynomial      91
Group      10
Group character      126
Group of units      49
Haar measure      134
Heisenberg group      16
Hensel's lemma      116
Homomorphism, group      13
Homomorphism, ring      48
Hypothesis H      288
Ideal      90 171
Image      16
Incongruent      45
Integer part      xi 28 206
Integer-valued polynomial      356 357
Integral domain      174
Integral operator      146
Invertible class      55
Involution      403
Isomorphism      13
Jacobi symbol      114
Jacobi's theorem      431
k-abundant number      260
Kernel      16
Kneser's theorem      397
L-function      330
Lagrange's theorem      69 355
Lame's theorem      25
Lattice point      233
Laurent polynomial      181
Leading coefficient      84
Least common multiple      28
Least nonnegative residue      46
Legendre symbol      101 153
Leibniz formula      119
Lexicographic order      9
Linear Diophantine equation      39
Liouville's formulae      402 419 420
Liouville's function      226
Ljunggren equation      42
localization      180
Logarithmic derivative      177
Logarithmic integral      298
Lower asymptotic density      256 360 482
m-adic representation      5
Mathematical induction      xii
Mean value      206
Mersenne prime      36 107 242
Mertens's formula      279
Mertens's theorem      276
Middle binomial coefficient      268
Minimum principle      3
Moebius function      217
Moebius inversion      218
Multiple      3
Multiplicative character      326
Multiplicative function      58 217 224 430
Multiplicatively closed      179
Nilpotent      56 172
Norm, $L^2$      134
Norm, $L^{\infty}$      137
NSE      367 376
Odd character      326
Odd function      401
Order      68
Order modulo m      83
Order of magnitude      xii 273
Order, group      69
Order, group element      70
Order, lexicographic, partial      10
Order, total      10
Orthogonality relations      129 130 327
p-adic value      27
p-group      121
Pairing      129
Pairwise relatively prime      13
Partial fractions      462
Partial order      10
Partial quotients      19
Partial summation      211
Partition      455
Partition function      455
Perfect number      241
Plaintext      76
Pointwise product      201
Pointwise sum      201
Polynomial      84
Polynomial, congruent      90
Polynomial, degree      84
Polynomial, derivative      116
Polynomial, monic      84
Polynomial, root      85
Polynomial, zero      85
Power      189
Power residue      98
Powerful number      32 187
Prime ideal      171
Prime number      25
Prime number race      351
Prime number theorem      274 289
Primitive abundant number      260
Primitive root      84
Primitive set      255
Principal character      151 326
Principal ideal      171
Principal ring      171
Product ideal      175
Projective space      15
Pseudoprime      75
Public key cryptosystem      76 78
Quadratic form      108 404
Quadratic nonresidue      98 101
Quadratic reciprocity law      109
Quadratic residue      98 100
Quotient      4
Quotient field      176 180
Quotient group      73
Radical      30 172 218
Radical ideal      172
Radical of an integer      172
Radical of polynomial      173
Ramanujan — Nagell equation      42
Real character      326
Reduced set of residues      54
Reflexive relation      9
Relatively prime      13
Remainder      4
Representation function      367
Residue class      46
Riemann hypothesis      323 351
Riemann zeta function      221 335
Ring      48
Ring of formal power series      205
Ring of fractions      180
Root of unity      11
RSA cryptosystem      79
Secret key cryptosystem      77
Selberg's formula      293 294
Set of multiples      255
Shnirel'man density      359
Shnirel'man's addition theorem      363
Sieve of Eratosthenes      34
Simple continued fraction      19
Spectrum      171
Square-free integer      32 217
Stable basis      359
Standard factorization      27
Subgroup      11
Sum function      206
Sumset      121 361
Support      137 291
Tauberian theorem      486
Taylor's formula      119
Ternary quadratic form      405
Theta function      453
Total order      10
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