THE NORMAL BEHAVIOR OF THE SMARANDACHE FUNCTION

Let S(n) be the smallest integer k so that nlk!. This is known as the Smarandache function and has been studied by many authors

On curves over finite fields with Jacobians of small exponent

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.Comment: V3. Small corrections; references update