DOI QR코드

DOI QR Code

POINTS ON MODULAR CURVES OVER FINITE FIELDS

  • JEON, DAEYEOL (Department of Mathematics education Kongju National University)
  • Received : 2015.05.08
  • Accepted : 2015.07.31
  • Published : 2015.08.15

Abstract

In this paper we propose a method of computing the number of points on the reduction of non-hyperelliptic modular curves of genus greater than or equal to 3 over finite fields.

Keywords

References

  1. E. Arbarello, M. Cornalba, P. A. Griffiths and J. Harris, Geometry of Algebraic Curves, Vol. I, Grundlehren Math. Wiss. 267, Springer-Verlag, New York, 1985.
  2. Y. Hasegawa and M. Shimura, Trigonal modular curves, Acta Arith., 88 (1999), 129-140. https://doi.org/10.4064/aa-88-2-129-140
  3. S. D. Galbraith, Equations for modular curves, Ph. D. Thesis, University of Oxford (1996).
  4. A. Ogg, Hyperelliptic modular curves, Bull. Soc. Math. France 102 (1974), 449-462.
  5. B. Saint-Donat, On Petri's analysis of the linear system of quadrics through a canonical curve, Math. Ann. 206 (1973), 157-175. https://doi.org/10.1007/BF01430982