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Newman D.J. — Analytic number theory

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Название: Analytic number theory

Автор: Newman D.J.

Аннотация:

Analytic Number Theory presents some of the central topics in number theory in a simple and concise fashion. It covers an amazing amount of material, despite the leisurely pace and emphasis on readability. The author's heartfelt enthusiasm enables readers to see what is magical about the subject. Topics included are: The Partition Function; The Erdös-Fuchs Theorem; Sequences without Arithmetic Professions; The Waring Problem; A "Natural" Proof of the Non-vanishing of L-Series, and a Simple Analytic Proof of the Prime Number Theorem - all presented in a surprisingly elegant and efficient manner with clever examples and interesting problems in each chapter. This text is suitable for a graduate course in analytic number theory.

Язык:

Рубрика: Математика/Теория чисел/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 78

Добавлена в каталог: 05.06.2005

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Предметный указатель

Addition problems      1—2
Affine property      41
Analytic functions, L-series as      63
Analytic method      1
Analytic number theory      1—14
Analytic proof of Prime Number Theorem      65—71
Approximation lemma, basic      42—47
Arithmetic progressions      41
Arithmetic progressions, dissection into      14
Arithmetic progressions, sequences without      41—47
Asymptotic formula      4
Basic approximation lemma      42—47
Cauchy criterion      71
Cauchy integral      23—24
Cauchy's theorem      18—19
Change making      2—5
Commutative operation      59
complex numbers      18
Contour integral, modified      66
Contour integration      46
Contours, infinite      65
Contours, infinite, 65
Convergence theorem      66
Convergence theorem, proof of      66—68
Crazy dice      5—8
Dice, crazy      5—8
Dirichlet series      59—60 62
Dirichlet theorem      45 50
Dissection into arithmetic progressions      14
Elliptic integral      33
Entire functions      60
Erdoes — Fuchs theorem      31 35—38
Erdoes, Paul      vii
Euler’s factorization      60
Euler’s factorization formula      71
Euler’s theorem      11—12
Evens and odds, dissection into      14
Extremal sets      42
Finite contours      65
Fourier analysis      65
Generating functions      1
Generating functions of asymptotic formulas      18—19
Generating functions of representation functions      7
Infinite contours      65
Integers      1
Integers, breaking up      17
Integers, nonnegative, splitting      8—10
L-series as analytic functions      63

L-series nonvanishing of      see Nonvanishing of L-series
L-series, general      61—62
L-series, zero of any      63
Lagrange theorem      49
Landau corollary      69
L’Hopital's rule      5
Mathematics      vii
Nonnegative integers, splitting      8—10
Nonvanishing of L-series      60
Nonvanishing of L-series, “natural” proof of      59—63
Odds and evens, dissection into      14
Parseval upper bound      36
Parseval’s identity      33—34
Partial fractional decomposition      3—4
Partition function      17—29
Permission constant      42
Pigeonhole Principle      50
PNT      see Prime Number Theorem
Prime Number Theorem (PNT)      65
Prime Number Theorem (PNT), analytic proof of      65—71
Prime Number Theorem (PNT), first proof of      68—70
Prime Number Theorem (PNT), second proof of      70—72
Pringsheim-Landau Theorem      59
Progressions, arithmetic      see Arithmetic progressions
q(n), coefficients of      25—29
Relative error      4
Representation functions      7
Representation functions, generating functions of      7
Representation functions, near constancy of      31
Riemann integral      20
Riemann integral, double      31
Riemann Sums      20—25
Roth theorem      46—47
Rulers, marks on      12—13
Schnirelmann’s Theorem      50—51
Schwarz inequality      34
Sequences without arithmetic progressions      41—47
Splitting problem      8—10
Stirling's formula      4 27 29
Szemeredi — Furstenberg result      43
Taylor coef?cients      3
Tchebychev's observation      70
Unit circle      13
Waring problem      49—56
Weyl sums      51—52
“Magnitude property”      53
“Monotone majorant”      45
“Natural” proof      59
“Natural” proof of nonvanishing of L-series      59—63

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