Elliptic Functions and Elliptic IntegralsThis book is devoted to the geometry and arithmetic of elliptic curves and to elliptic functions with applications to algebra and number theory. It includes modern interpretations of some famous classical algebraic theorems such as Abel's theorem on the lemniscate and Hermite's solution of the fifth degree equation by means of theta functions. Suitable as a text, the book is self-contained and assumes as prerequisites only the standard one-year courses of algebra and analysis. |
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Elliptic Functions and Elliptic Integrals Viktor Vasil_evich Prasolov,I_Uri_ Pavlovich Solov_ev No preview available - 1997 |
Common terms and phrases
a₁ Abel's theorem addition of points addition theorem arc length automorphism ax² b₁ calculations change of parameter change of variables coefficients complex numbers construct coordinates corresponds cubic equation curve y² degree equation degree polynomial distinct divisible easy to verify elements elliptic curve elliptic function elliptic integrals equal equation y² expressed in terms Fermat primes Figure finite follows formula fundamental parallelogram Hence infinite point inflection points integer solution intersection points irreducible irreducible polynomial isomorphism k² sin² k²x² lattice lemniscate linear meromorphic Moreover nonsingular cubic nonzero numbers P₁ parameterization poles problem proof quadratic quintic equation r₁ radicals rational function rational numbers rational point rational solutions relation relatively prime root of unity ruler and compass Serret's curves singular points solvable solve straight line subgroup suffices tangent transformation values Weierstrass function y₁ zero