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Elliptic Tales by Robert Gross, Avner Ash

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Chapter 11

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BUILDING FUNCTIONS

Road Map

Fortified with our understanding of degree, together with some of the algebra of elliptic curves and abelian groups, we must now acquire more tools in order to understand the statement of the BSD Conjecture. Our first task is to take a sequence of numbers and use those numbers to construct functions.

1. Generating Functions

The number theory discussed in this book concerns counting the number of solutions to systems of equations of various kinds. For example, in Part I, we counted the number of solutions to a system of two polynomial equations. We discussed Bézout’s Theorem, which tells us how many solutions ...

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