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Newman D.J. — Analytic number theory |
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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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