By Torsten Ekedahl

Those lecture notes grew out of a one semester introductory path on elliptic curves given to an viewers of laptop technological know-how and arithmetic scholars, and suppose purely minimum historical past wisdom. After having coated uncomplicated analytic and algebraic elements, placing certain emphasis on explaining the interaction among algebraic and analytic formulation, they pass directly to a few extra really expert subject matters. those contain the $j$-function from an algebraic and analytic viewpoint, a dialogue of elliptic curves over finite fields, derivation of recursion formulation for the department polynomials, the algebraic constitution of the torsion issues of an elliptic curve, complicated multiplication, and modular varieties. which will inspire uncomplicated difficulties the ebook starts off very slowly yet considers a few points akin to modular sorts of better point which aren't frequently taken care of. It offers greater than a hundred routines and a Mathematica TM computing device that treats a couple of calculations related to elliptic curves. The e-book is geared toward scholars of arithmetic with a normal curiosity in elliptic curves but additionally at scholars of computing device technology drawn to their cryptographic elements. A book of the ecu Mathematical Society (EMS). disbursed in the Americas by way of the yankee Mathematical Society.

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