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Elliptic Tales by Robert Gross, Avner Ash

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Chapter 14

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SURPRISING PROPERTIES OF L-FUNCTIONS

Road Map

Now that we have constructed the L-function associated to an elliptic curve, we focus our attention on the analytic properties of this function. We delay our consideration of how the L-function might capture some of the properties of the elliptic curve until the next chapter.

1. Compare and Contrast

The L-functions defined in the preceding chapter are not obviously functions of the complex variable s, although we told you they were. For example, let E be an elliptic curve defined over Q. To state the BSD Conjecture, it is essential to view L(E, s) as an actual function, not just a formal ...

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