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The analytic rank of a curve or abelian variety is the order of vanishing of its L-function at the central value. It is difficult to compute the order of vanishing exactly, but it can be bounded above by counting zeros in a small interval about the central point. By making this interval sufficiently small one obtains a bound that is conjecturally tight, and this can be proved when the rank is 0 or 1.

Knowl status:
  • Review status: reviewed
  • Last edited by John Cremona on 2018-05-23 16:28:30.304000