√лавна€    Ex Libris     ниги    ∆урналы    —татьи    —ерии     аталог    Wanted    «агрузка    ’удЋит    —правка    ѕоиск по индексам    ѕоиск    ‘орум   
blank
јвторизаци€

       
blank
ѕоиск по указател€м

blank
blank
blank
 расота
blank
Edwards H.M. Ч Riemann's Zeta Function
Edwards H.M. Ч Riemann's Zeta Function

„итать книгу
бесплатно

—качать книгу с нашего сайта нельз€

ќбсудите книгу на научном форуме



Ќашли опечатку?
¬ыделите ее мышкой и нажмите Ctrl+Enter


Ќазвание: Riemann's Zeta Function

јвтор: Edwards H.M.

јннотаци€:

Edwards elaborates on Bernard Riemann's eight-page paper On the Number of Primes Less Than a Given Magnitude, published in German in 1859. His goal is not to supplant the classic work, but to provide mathematics students access to it. Indeed an English translation of the original is appended. Academic Press published the 1974 edition.


язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 2001

 оличество страниц: 330

ƒобавлена в каталог: 04.05.2008

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
blank
ѕредметный указатель
Abel integral formula for $\zeta(s)$      9 221
Abel's theorem      278
Alpha notation for roots $\rho=1/2+ia$      36
Analytic continuation of a particular integral      276Ч277
Analytic continuation of zeta function      11 16n 115
Analytic continuation, Riemann's conception of      9
Approximate functional equation      Hardy and Littlewood
as consequence of Riemann hypothesis      188
Asymptotic expansions      Euler-Maclaurin summation for evaluation of zeta Logarithmic Riemann Stirling's 87
Backlund      97
Backlund determination of N(T) for T=200      128Ч129
Backlund estimation of N(T)      132Ч134
Backlund theorem on Lindelof hypothesis      182 188Ч190
Bernoulli numbers      11 103
Bernoulli numbers $B_{2n+1}=0$      11n 14n 103
Bernoulli polynomials $B_n(x)$      100Ч103
Bernoulli polynomials $B_n(x)$ periodified $\overline{B}_n(x)$      104
Bohr and Landau Riemann hypothesis implies S unbounded      181 201Ч202
Bohr and Landau theorem on roots near Re s=1/2      19 193Ч195
Bombieri      297
Cesaro averages      279
Chebyshev estimates of $\pi$ from estimates of $\psi$      68 76Ч77
Chebyshev estimation of $\pi (x)$      3Ч4 281Ч284
Chebyshev mentioned by Riemann      5
Chebyshev's identity      281Ч284
Conditional convergence in Fourier analysis      23
Conditional convergence of sums over $\rho$      20Ч21 30 35 49Ч50
DE LA VALLEY POUSSIN estimate of error in prime number theorem      78Ч95
DE LA VALLEY POUSSIN proof of prime number theorem      68
DE LA VALLEY POUSSIN proof that $\sum \mu(n)/n=0$      91Ч95
Debye      139
Definite integrals      Riemann evaluation
Denjoy      268Ч269
Dirichlet      298 299
Dirichlet acquaintanceship with Chebyshev      4
Dirichlet use of Euler product formula      7
Erdos      282 288
Euclid      1
Euler $\phi$-function      250Ч251
Euler $\Sigma p^{-1}$ diverges      1
Euler and factorial function      7Ч8
Euler and functional equation of zeta      12
Euler formula $\sum^{\infty}_{n=-\infty} x^{n}=0$      212
Euler product formula      Euler 1 6Ч7 22Ч23 50n
Euler statement of $\Sigma \mu(n)/n=0$      92
Euler Ч Maclaurin summation      Stirling's series 97
Euler Ч Maclaurin summation for evaluation of zeta      114Ч115
Euler Ч Maclaurin summation statement of method      98Ч106
Euler Ч Maclaurin summation summary of method      106
Euler's constant      67 106n
Explicit formulas      J function psi
Factorial function      Stirling's series 7Ч9
Farey series      263Ч264
Farey series related to Riemann hypothesis      264Ч267
Fourier analysis      23Ч25 203Ч225
Fourier analysis adjoint of an operator      205
Fourier analysis inversion formulas      24 27 51 54Ч56 205 213Ч215
Fourier analysis transform of an (invariant) operator      204
Fourier analysis, interpretation of Chebyshev's identity      282Ч283
Fourier series of $\overline{B_1}(x)$      196
Fourier transform      Fourier analysis transform 209 211
Franel and Landau Farey series and the Riemann hypothesis      263Ч267
G function      206
G function functional equation      209Ч210
Gamma function      Factorial function
Gauss      299 305
Gauss counts of primes      2 305
Gauss notation $\prod$ for factorial      8
Gauss on density of primes      2
Gram computation of 15 roots $\rho$      96Ч97
Gram points      125Ч126
Gram's law      127 171
Gram's law exceptions      126Ч127 176n
Gram's law statement of      126
H function      207
Hadamard proof of prime number theorem      6 38 68
Hadamard proof of product formula for $\xi$      18 21 39
Hadamard proof that $\zeta(l+it)\neq 0$      69Ч72
Hadamard publication of three circles theorem      187
Hardy      136
Hardy and Littlewood approximate functional equation      201n 229n
Hardy and Littlewood average of $(|\zeta(s)|)^{3}$ on Re=const      195
Hardy and Littlewood estimate of $\zeta(1/2)$      201
Hardy and Littlewood KT roots on Re s=1/2      19 226 229Ч237
Hardy and Littlewood reformulation of Lindelof hypothesis      201
Hardy and Littlewood Tauberian theorems for Cesaro averages      279
Hardy and Littlewood use of Tauberian theorem to prove prime number theorem      280
Hardy infinitely many roots on Re s=1/2      19 226Ч229
Haselgrove      96 121 157 161 178
Haselgrove excerpts from tables      122Ч123 158
Haselgrove on exceptions to Gram's law      126n
hilbert      6 298
Hutchinson      97
Hutchinson numerical analysis of roots $\rho$      126Ч127 129Ч132
Ikehara's theorem      281
J function      22
J function in terms of $\pi(x)$      33
J function Riemann's formula for      33 48 61Ч65
jacobi      15
Jensen's theorem      39Ч41
KUZMIN proof of Riemann Ч Siegel integral formula      273Ч278
Landau      62 62n 136
Landau average of $(|\zeta(s)|)^2$ on Re=const      195
Landau o, O notation      Bohr and Landau Franel 200
Legendre notation for gamma function      8
Legendre on density of primes      3
Legendre relation for factorial function      9
Lehman      269
Lehman verification of Riemann hypothesis to g_{250000}      172
Lehmer's phenomenon      179
Lehmer, D. H. computations of roots $\rho$      175Ч179
Lehmer, D. H. on Riemann's formula for $\pi(x)$      35
Lehmer, D. H. verification of Riemann hypothesis to g_{250000}      172
Lehmer, D. N. counts of primes      3
Levinson      288
Li(x)      Logarithmic integral
Lindelof estimates of growth of $\zeta(s)$      182Ч186
Lindelof hypothesis      186 177n 188 201
Lindelof's theorem      184
Lindelof's theorem modified      186
LITTLEWOOD $\int^T_0 S(t)dt=O(log T)$      173
LITTLEWOOD $\pi(x)<Li(x)$ fails      269
LITTLEWOOD improvement of $\beta<1$      200
LITTLEWOOD improvement of Bohr Ч Landau theorem      195
LITTLEWOOD improvement of Tauber's theorem      279
LITTLEWOOD Riemann hypothesis and growth of M      261
LITTLEWOOD use of three circles theorem      Hardy and Littlewood 187
Logarithmic integral Li(x)      26
Logarithmic integral Li(x) asymptotic formula for      86
Logarithmic integral Li(x) estimate of $Li(x^p)$ as $x\longrightarrow\infty$      90
Logarithmic integral Li(x) value at $x^{\beta}$ for complex $\beta$      30
M function (sum of Mobius $\mu$)      260
Maclaurin      Euler-Maclaurin summation
mellin      25n
Mellin estimate of $\zeta(l+it)$      183
Mertens proof that $\zeta(l+it)\neq 0$      79Ч80
Mertens's theorem      6
Mobius inversion      34 217Ч218 283 285
Mu function of Lindelof $\mu(\sigma)$      186
Mu function of Mobius $\mu(n)$      34 91Ч92 217
N function      128
N function Backhand's verification of Riemann's estimate      132Ч134
N function evaluated by Turing's method      172Ч175
Nonsense      212 217
O, o notation      200
Parseval's equation      215Ч216
Pi function $\pi(x)$      4 33
Pi function $\pi(x)$ approximations to      84Ч91
Pi function $\pi(x)$ in terms of J (x)      Prime number theorem Poisson summation formula 34 209Ч210
Polya theorems on functions with zeros on Re s=1/2      269Ч273
Prime number theorem      4
Prime number theorem improved remainder      84 200
Prime number theorem proof      68Ч77
Product formula for $\xi(s)$      20Ч21
Product formula for $\xi(s)$ proof      46Ч47
Product formula for sine      9 18 47 224
Psi function $\psi(x)$ of Chebyshev      49
Psi function $\psi(x)$ of Chebyshev, von Mangoldt's formula for      Chebyshev 49Ч61
Ramanujan's formula      218Ч225
Rho      Roots $\rho$
RIEMANN "everywhere valid" formula for $\zeta(s)$      9Ч11
RIEMANN analytic functions treated globally      20
RIEMANN comments on $\pi(x)\sim Li(x)$      34Ч36 269 305
RIEMANN computations of roots      159Ч162
RIEMANN error involving $\xi(0)$      31
RIEMANN estimate of N(T)      18Ч19 301
RIEMANN evaluation of definite integrals      12Ч13 19 26Ч33 146Ч148
RIEMANN explicit formula for J(x) (=f(x))      33 304
Riemann hypothesis      6 19
Riemann hypothesis in light of Riemann Ч Siegel formula      164Ч166
Riemann hypothesis probabilistic interpretation      268Ч269
Riemann hypothesis, implies Lindelof hypothesis      188
Riemann hypothesis, related to error in prime number theorem      88Ч91
Riemann hypothesis, related to Farey series      263Ч267
Riemann hypothesis, related to growth of M(x)      260Ч263
Riemann hypothesis, verified to $T=g_{1040}$      171
Riemann hypothesis, verified to $T=g_{250000}$      172
Riemann hypothesis, verified to $T=g_{25000}$      172
Riemann hypothesis, verified to $T=g_{3500000}$      172 179Ч180
Riemann hypothesis, verified to T=200      129
Riemann hypothesis, verified to T=300      129Ч132
RIEMANN introduction of function $\xi$      16
RIEMANN manuscript with statement of asymptotic formula      156Ч157
RIEMANN paper on $\pi(x)$      1Ч38
RIEMANN proofs of the functional equation      12Ч16 166Ч170 274 300Ч301
RIEMANN questions unresolved by      37Ч38
RIEMANN skill as analyst      136
RIEMANN statement of Riemann hypothesis      19 30n 301
RIEMANN translation of paper on $\pi(x)$      299Ч305
RIEMANN use of "Fouriers theorem"      23Ч25 302Ч303
RIEMANN use of saddle point method      139n
RIEMANN view of analytic continuation      9 20
Riemann Ч Siegel asymptotic formula      136Ч164
Riemann Ч Siegel asymptotic formula error estimates      162Ч164
Riemann Ч Siegel asymptotic formula manuscript      156Ч157
Riemann Ч Siegel asymptotic formula statement      154
Riemann Ч Siegel integral formula      137 166Ч170
Riemann Ч Siegel integral formula proof by Kuzmin      273Ч278
Riemann's estimate      18Ч19 301
Riemann's estimate of density      Conditional convergence Bohr 21 43 302
Roots $\rho$ of $\xi(s)=0$      18Ч19
Roots $\rho$ of $\xi(s)=0$ computations of      96 157Ч162 178
Roots $\rho$ of $\xi(s)=0$ crude estimate of density      42Ч43
Roots $\rho$ of $\xi(s)=0$ real parts<1      1 70Ч72 79Ч81 200
Roots $\rho$ of $\xi(s)=0$ von Mangoldt's estimate of density      56Ч58
Rosser's rule      180Ч181
Rosser, YOHE, and SHOENFELD error estimate for Riemann Ч Siegel formula      163
Rosser, YOHE, and SHOENFELD use of Turing's method      175 180
Rosser, YOHE, and SHOENFELD verification of Riemann hypothesis to $T=g_{3500000}$      179Ч180
S function S(T)      173
S function S(T) estimates of      174 190Ч193 201Ч202
Saddle point method      139Ч140
Selberg elementary proof of prime number theorem      282 288Ч297
Selberg KT log T roots on Re s=1/2      19 226 237Ч259
Selberg's inequality      284Ч288
Self-reciprocal operators      210Ч211
Siegel discovery of Riemann Ч Siegel formula      136
Siegel discovery of Riemann Ч Siegel formula proof that Riemann Ч Siegel formula is asymptotic      163
Slit plane      111
Steepest descent, method of      139Ч140
STIELTJES alleged proof of Riemann hypothesis      262Ч263
STIELTJES estimate of remainder in Stirling's series      112
STIELTJES evaluation of the constant in Stirling's series      113
Stirling      109
Stirling's formula      Stirling's series
Stirling's series      106Ч114
Stirling's series for $\prod'(s)/\prod(s)$      113
Stirling's series statement      109
Stirling's series Stieltjes's estimate of the remainder      112
Tauber      278
Tauberian theorems      278Ч281
Theta function $\Theta$ of Chebyshev      76 288
Theta function $\upsilon(t)$ in $\zeta(1/2+it)=Z(t)$ exp i $\upsilon(t)$      119
Theta function $\upsilon(t)$ in $\zeta(1/2+it)=Z(t)$ exp i $\upsilon(t)$ asymptotic formula for      120Ч121
Theta function of Jacobi      15 170 227
Three circles theorem      187
TlTCHMARSH as secondary source      199 226
TlTCHMARSH average of $\zeta(1/2+ig_n)$ is 2      229
TlTCHMARSH error estimate for Riemann Ч Siegel formula      162Ч163
TlTCHMARSH verification of Riemann hypothesis to T=g_1040      171
Turing's method of evaluating N(T)      172Ч175
Vinogradov's estimate of $\zeta(l+it)$      200
von Mangoldt estimate of N(T)      173
von Mangoldt proof of formula for $\psi$      50Ч61
von Mangoldt proof of Riemann's estimate of N(T)      133
von Mangoldt proof of Riemann's formula for J(x)      48 61Ч65
von Mangoldt proof that $\sum \mu(n)/n$      0 92
von Mangoldt statement of formula for $\psi$      49 54 66
Weil      298
Weyl's estimates of $\zeta(l+it)$      200
Wiener's Tauberian theorem      280Ч281
Wirsing      288 294 297
Xi function $\xi(s)$      16Ч18
Xi function $\xi(s)$ as transform of self-adjoint operator      206Ч213
Xi function $\xi(s)$ rate of growth      41
Z function Z(t)      119
Z function Z(t) asymptotic formula for      Riemann Ч Siegel asymptotic formula 119
Zeta function analytic continuation of      9Ч11 16n
Zeta function as Fourier transform of summation operator      204
Zeta function evaluation by Euler Ч Maclaurin summation      114Ч118
Zeta function growth in strip $0\leq Re\ s\leq 1$      182Ч201
Zeta function growth related to zeros      182 188 190 193 200
Zeta function value of $\zeta'(0)/\zeta(0)$      66Ч67 134Ч135
Zeta function values at integers      11Ч12
Zeta function values at negative integers      216Ч217
Zeta function, functional equation      Euler Riemann 12Ч16 222 224Ч225
blank
–еклама
blank
blank
HR
@Mail.ru
       © Ёлектронна€ библиотека попечительского совета мехмата ћ√”, 2004-2017
Ёлектронна€ библиотека мехмата ћ√” | Valid HTML 4.01! | Valid CSS! ќ проекте