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Weierstrass points on hyperelliptic modular curves

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In this paper, we find all Weierstrass points on the hyperelliptic modular curves $X_1(N)$.

Abstract

In this paper, we find all Weierstrass points on the hyperelliptic modular curves $X_1(N)$.

참고문헌 (15)

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  2. 최소영, "A Weierstrass point of Γ₁(4p)", 충청수학회지, 21(4), pp.467~470 (2008), 충청수학회
  3. F. Diamond, "A First Course in Modular Forms, Graduate Texts in Mathematics", pp.436~ (2005), Springer-Verlag
  4. N. Ishii, "Hyperelliptic modular curves", Tsukuba J. Math, 15(2), pp.413~423 (1991)
  5. D. Jeon, "Bielliptic intermediate modular curves", Preprint, ~
  6. K. Kilger, "Weierstrass points on X0(pl) and arithmetic properties of Fourier coefficients of cusp forms", Ramanujan J, 17(3), pp.321~330 (2008)
  7. W. Kohnen, "Weierstrass points at cusps on special modular curves", Abh. Math. Sem. Univ. Hamburg, 73, pp.241~251 (2003)
  8. W. Kohnen, "A short remark on Weierstrass points at infinity on X0(N)", Monatsh. Math, 143(2), pp.163~167 (2004)
  9. J. Lehner, "Weierstrass points of Γ0(N)", Ann of Math, 79, pp.360~368 (1964)
  10. J. -F. Mestre, "Corps euclidiens, unit´es exceptionnelles et courbes ´elliptiques", J. Number Theory, 13(2), pp.123~137 (1981)
  11. A. P. Ogg, "Rational points on certain elliptic modular curves, Analytic number theory", Pro. Sympos. Pure Math, pp.221~231 (1972), Amer. Math. Soc.
  12. A. P. Ogg, "On the Weierstrass points of X0(N)", Illinois J. Math, 22(1), pp.31~35 (1978)
  13. K. Ono, "The web of modularity: arithmetic of the coefficients of modular forms and q-series", CBMS Regional Conference Series in Mathematics (2004), Amer. Math. Soc.
  14. D. Rohrlich, "Weierstrass points and modular forms", Illinois J. Math, 29(1), pp.131~141 (1985)
  15. B. Sch¨oneberg, "Uber die Weierstrasspunkte in den K¨orpern der elliptischen Modulfunktionen", Abh. Math. Sem. Univ. Hamburg, 17, pp.104~111 (1951)

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