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Paper   IPM / M / 16496
School of Mathematics
  Title:   On the curve YN=X\Ell(XM+1) over finite fields
  Author(s):  Saeed Tafazolian
  Status:   To Appear
  Journal: Advances in Mathematics of Communications
  Supported by:  IPM
  Abstract:
Let \cX be the nonsingular model of a plane curve of type yn=f(x) over the finite field \F of order q2, where f(x) is a separable polynomial of degree coprime to n. If the number of \F-rational points of \cX attains the Hasse-Weil bound, then the condition n divides q+1 is equivalent to the solubility of f(x) in \F []. In this paper, we investigate this condition for f(x)=xl(xm+1).

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