## 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 |

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Abel's theorem addition of points addition theorem algebraic curves arc length automorphism calculations change of parameter change of variables coefficients complex numbers construct coordinates corresponds cosp cubic equation curvey degree equation degree polynomial distinct divisible divisor easy to verify elements elliptic curve elliptic function elliptic integrals equal equation 5.1 expressed in terms Fermat primes Figure finite follows formula function f function p(z fundamental parallelogram Hence infinite point inflection points integer solution intersection points irreducible irreducible polynomial isomorphism lattice lemniscate Let us show linear meromorphic Moreover nonsingular cubic nonzero numbers obtained parameterization poles problem projective plane proof psin quintic equation radicals rational function rational numbers rational point rational solutions relation relatively prime root of unity ruler and compass Serret's curves sing singular points ſº solvable straight line subgroup suffices tangent theory transformation values Weierstrass function zero