Elliptic Curves: Diophantine Analysis

ISBN-13: 9783642057175 / Angielski / Miękka / 2010 / 264 str.

S. Lang

Opis

This book takes the view that parallel to the pure arithmetic theory over number fields lies the algebraic-geometric theory of algebraic systems, where sections play the role of rational points. The author formulates analogs of classic diophantine problems.

Spis treści

I. General Algebraic Theory.- I. Elliptic Functions.- II. The Division Equation.- III. p-Adic Addition.- IV. Heights.- V. Kummer Theory.- V1. Integral Points.- II. Approximation of Logarithms.- VII. Auxiliary Results.- VIII. The Baker—Feldman Theorem.- IX. Linear Combinations of Elliptic Logarithms.- X. The Baker—Tijdeman Theorem.- XI. Refined Inequalities.