Riemann's Zeta FunctionCourier Corporation, 01.01.2001 - 315 Seiten Superb high-level study of one of the most influential classics in mathematics examines landmark 1859 publication entitled “On the Number of Primes Less Than a Given Magnitude,” and traces developments in theory inspired by it. Topics include Riemann's main formula, the prime number theorem, the Riemann-Siegel formula, large-scale computations, Fourier analysis, and other related topics. English translation of Riemann's original document appears in the Appendix. |
Inhalt
III | 1 |
IV | 6 |
V | 7 |
VI | 9 |
VII | 11 |
VIII | 12 |
IX | 15 |
X | 16 |
LV | 134 |
LVI | 136 |
LVII | 137 |
LVIII | 141 |
LIX | 145 |
LX | 148 |
LXI | 155 |
LXII | 162 |
XI | 18 |
XII | 20 |
XIII | 22 |
XIV | 23 |
XV | 25 |
XVI | 26 |
XVII | 29 |
XVIII | 31 |
XIX | 33 |
XX | 36 |
XXI | 37 |
XXII | 39 |
XXIII | 40 |
XXIV | 41 |
XXV | 42 |
XXVII | 43 |
XXVIII | 45 |
XXIX | 46 |
XXX | 48 |
XXXI | 50 |
XXXII | 54 |
XXXIII | 56 |
XXXIV | 58 |
XXXV | 61 |
XXXVI | 62 |
XXXVII | 66 |
XXXVIII | 68 |
XXXIX | 70 |
XL | 72 |
XLI | 76 |
XLII | 78 |
XLIII | 79 |
XLIV | 81 |
XLV | 84 |
XLVI | 88 |
XLVII | 91 |
XLVIII | 96 |
XLIX | 98 |
L | 106 |
LI | 114 |
LII | 119 |
LIII | 127 |
LIV | 132 |
LXIII | 164 |
LXIV | 166 |
LXV | 171 |
LXVI | 172 |
LXVII | 175 |
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LXIX | 182 |
LXX | 183 |
LXXI | 187 |
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LXXIII | 190 |
LXXIV | 193 |
LXXV | 195 |
LXXVI | 199 |
LXXVII | 203 |
LXXVIII | 205 |
LXXIX | 206 |
LXXX | 209 |
LXXXI | 212 |
LXXXII | 213 |
LXXXIII | 215 |
LXXXIV | 216 |
LXXXV | 217 |
LXXXVI | 218 |
LXXXVII | 226 |
LXXXVIII | 229 |
LXXXIX | 237 |
XC | 246 |
XCI | 260 |
XCIII | 263 |
XCIV | 268 |
XCV | 269 |
XCVII | 273 |
XCVIII | 278 |
XCIX | 281 |
C | 284 |
CI | 288 |
CII | 298 |
CIII | 299 |
CIV | 306 |
311 | |
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Häufige Begriffe und Wortgruppen
analytic continuation analytic function approaches zero approximation average B₂ Backlund bounded C₁ Chebyshev circle coefficients computations const constant times log converges defined definite integral denote derivative dy(x estimate Euler Euler product Euler-Maclaurin summation evaluation fact Farey series follows formula for J(x Fourier functional equation gives Gram points Gram's law halfplane hence imaginary implies inequality infinite integrand interval Lehmer less Li(x limit Lindelöf hypothesis Lindelöf's theorem line Res Littlewood log II(s log(s logarithmic derivative Math method Möbius inversion modulus number of roots O(log operator f(x pole positive real prime number theorem product formula proof range real axis real numbers relative error Riemann hypothesis Riemann-Siegel formula right side shown shows statement Stieltjes Stirling's formula Stirling's series sufficiently large term omitted termwise integration theory tion Titchmarsh transform valid Vallée Poussin's zeta function Σπί