Bernhard Riemann Collected Papers 0974042722, 0974042730
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English Pages 567 Year 2004
Table of contents :
Preface
Contents
I.(1867) Foundations for a general theory of functions of a complex variable (Inaugural dissertation, Göttingen 1851; second printing (unchanged), Göttingen 1867.)
II.(1854) On the laws of distribution of electric charge in a ponderable body that is neither a perfect conductor nor insulator, but may be viewed as resisting the holding of electric charge with finite power (Official report of the 31st assembly of German scientific researchers and physicians, Göttingen, September 1854.)
III.(1855) On the theory of Nobili's color rings (Poggendorff's Annalen der Physik und Chemie, vol. 95, March 28, 1855.)
IV.(1857) Contributions to the theory of the functions represented by the Gauss series F(α, β, γ, x) (Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen, VII, 1857.)
V.(1857) Author's announcement of the preceding paper (Gottinger Nachrichten, 1857, no. 1)
VI.(1857) The Theory of Abelian Functions (Borchardt's Journal für reine und angewandte Mathematik, vol. 54, 1857.)
VII.(1859) On the number of primes less than a given magnitude (Monatsberichte der Berliner Akademie, November 1859.)
VIII.(1860) On the propagation of planar air waves of finite amplitude (Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen, vol. 8, 1860.)
IX.(1859 )Author's announcement for VIII (Göttinger Nachrichten, 1859, no. 19.)
X.(1861) A contribution to the study of the motion of a homogeneous fluid ellipsoid (Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen, vol. 9, 1861.)
XI.(1865) On the vanishing of Θ-functions (Borchardt's Journal für reine und angewandte Mathematik, vol. 65, 1865.)
XII. On the representation of a function by a trigonometric series (Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen, vol. 13.)
XIII. The hypotheses on which geometry is based (Königlichen Gesellschaft der Wissenschaften zu Göttingen, vol. 13.)
XIV. A contribution to electrodynamics (Poggendorff 's Annalen der Physik und Chemie, vol. 131.)
XV. A proof of the theorem that a single-valued periodic function of n variables cannot be more than 2n-fold periodic (Extract from a letter from Riemann to Weierstrass.)(Borchardt's Journal für reine und angewandte Mathematik, vol. 71.)
XVI. Extract from a letter written in Italian on January 21, 1864 to Professor Enrico Betti (Annali di Matematica, Ser. 1, vol. 7.)
XVII. On the surface of least area with a given boundary (Königlichen Gesellschaft der Wissenschaften zu Göttingen, vol. 13.)
XIX. An attempt to generalize integration and differentiation
XX. New theory of residual charge in apparatus for static charge
XXI.(1857) Two general theorems on linear differential equations with algebraic coefficients (20th February 1857.)
XXII. A mathematical work that seeks to answer the question posed by the most distinguished academy of Paris
Weber's remarks on XXII
XXIII. On the representation of the quotient of two hypergeometric series as an infinite continued fraction
XXIV. On the potential of a ring
XXV. Diffusion of heat in an ellipsoid
XXVI. Equilibrium of electricity on cylinders with circular cross-section and parallel axes. Conformal mapping of figures bounded by circles
XXVII. Examples of surfaces of least area with a given boundary
XXVIII. Fragments concerning limiting cases of the elliptic modular functions
Commentary on XXVIII. R. Dedekind
XXIX. Fragment on Analysis Situs
XXX. Convergence of p-fold infinite theta-series
XXXI. On the theory of Abelian functions
The life of Bernhard Riemann -- R. Dedekind
Notes on the Individual Papers
I, II, III
IV, V
VI
VII, VIII
IX, X, XI
XII
XIII, XIV
XV, XVI
XVII, XIX, XX
XXI, XXII
XXIII, XXIV, XXV
XXVI, XXVII, XXVIII, XXIX
XXX, XXXI, Natural Philosophy
The life of Bernhard Riemann
Bibliography
