For elliptic curves over $\Q$, a natural normalization for its L-function is the one that yields a functional equation $s\leftrightarrow 2-s.$ This is known as the *arithmetic normalization*, because the the Dirichlet coefficients are rational integers.
We emphasize that the arithmetic normalization is being used by writing
the L-function as $L(E,s)$. In this notation, the central point is at $s=1.$
The **special value** is the first non-zero value among $L(E,1), L'(E,1), L''(E,1), \ldots $

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- Review status: reviewed
- Last edited by John Jones on 2018-06-19 15:38:28

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- 2018-06-19 15:38:28 by John Jones (Reviewed)