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WEIERSTRASS POINTS ON Γ0(p) AND ITS APPLICATION

최도훈
대한수학회 (The Korean Mathematical Society)|2008.10|대한수학회논문집 (Communications of the KMS)|제23권 제4호|pp. 479-485

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키워드

modular formsone variablecongruences for modular forms
주제분류수학

초록

In this note, we study arithmetic properties for the exponents of modular forms on Γ0(p) for primes p. Our aim is to refine the result of [4] by using the geometric property of the modular curve of Γ0(p).

Abstract

In this note, we study arithmetic properties for the exponents of modular forms on Γ0(p) for primes p. Our aim is to refine the result of [4] by using the geometric property of the modular curve of Γ0(p).

참고문헌 (9)

  1. S. Ahlgren, "The theta-operator and the divisors of modular forms on genus zero subgroups", Math. Res. Lett, 10, pp.787~798 (2003)
  2. S. Ahlgren, "Weierstrass points on X0(p) and supersingular j-invariants", Math. Ann, 325(2), pp.355~368 (2003)
  3. J. Bruinier, "The arithmetic of the values of modular functions and the divisors of modular forms", Compos. Math, 140, pp.552~566 (2004)
  4. D. Choi, "On values of a modular form on Γ0(N)", Acta Arith, 121(4), pp.299~311 (2006)
  5. S. Choi, "The values of modular functions and modular forms", Canad. Math. Bull, 49(4), pp.526~535 (2006)
  6. W. Eholzer, "Product expansions of conformal characters", Phys. Lett. B, 388(1), pp.82~89 (1996)
  7. H. M. Farkas, "Riemann Surfaces" (1992), Springer-Verlag
  8. A. Ogg, "On the Weierstrass points of X0(N)", Illinois J. Math, 22(1), pp.31~35 (1978)
  9. J.-P. Serre, "Divisibilite des coefficients des formes modulaires de poids entier", C. R. Acad. Sci. Paris Ser. A, 279, pp.679~682 (1974)

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