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Elliptic Tales by Robert Gross, Avner Ash

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Preface

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As the pilgrims in Chaucer’s Canterbury Tales make their way across England to the shrine of St. Thomas Becket in Canterbury, they tell each other all sorts of stories. The aim of Elliptic Tales is to tell a variety of mathematical stories, in some depth but at a leisurely pace, relating a few of the beautiful ideas that have been developed to study the solutions of certain cubic equations called “elliptic curves.”

The goal of this book is to explain the conjecture of British mathematicians Bryan Birch (1931–) and Peter Swinnerton-Dyer (1927–), made in the 1960s, about the number of solutions to these cubic equations. This is usually referred ...

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