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On curves over finite fields with Jacobians of small exponent

Kevin Ford·Igor Shparlinski
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Abstract

We show that finite fields over which there is a curve of a given genus g with its Jacobian having a small exponent, are very rare. This extends a recent result of W. Duke in the case g=1. We also show when g=1 or g=2 that our bounds are best possible.

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Kevin Ford, Igor Shparlinski. 2008-09-21. On curves over finite fields with Jacobians of small exponent. https://arxiv.org/abs/math/0607474

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