id: 02319797
dt: b
an: 1998b.01052
au: McKean, Henry; Moll, Victor
ti: Elliptic curves. Function theory, geometry, arithmetic.
so: Cambridge University Press, Cambridge (ISBN 0-521-58228-8). 293 p. (1997).
py: 1997
pu: Cambridge University Press, Cambridge
la: EN
cc: F65
ut: elliptic functions; elliptic integrals; modular functions; modular groups;
theta functions; icosahedron; quintic equation; imaginary quadratic
number fields
ci:
li:
ab: The subject of elliptic curves is one of the jewels of nineteenth-century
mathematics, originated by Abel, Gauss, Jacobi, and Legendre. This book
presents an introductory account of the subject in the style of the
original discoverers, with references to and comments about more recent
and modern developments. The treatment combines three of the
fundamental themes of mathematics: complex function theory, geometry,
and arithmetic. After an informal preparatory chapter on rational
functions, Riemann surfaces, and the like, the book follows a
historical path, beginning with practical examples of elliptic
integrals and the discovery of Abel and Gauss that the inversion of
such an integral yields an elliptic function. This is followed by
chapters on Jacobi’s theta functions, modular groups and modular
functions, Abel’s and Hermite’s work on the quintic, Kronecker and
Weber’s imaginary quadratic field, and the Mordell-Weil theorem on
the rational points of elliptic curves. (orig.)
rv: