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Linear relations between modular forms for Г0+(p)

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We find linear relations among the Fourier coefficients of modular forms for the group Г0+(p) of genus zero. As an application of these linear relations, we derive congruence relations satisfied by the Fourier coefficients of normalized Hecke eigenforms.
Wydawca
Czasopismo
Rocznik
Tom
13
Numer
1
Opis fizyczny
Daty
otrzymano
2014-10-24
zaakceptowano
2015-09-17
online
2015-10-19
Twórcy
autor
  • Department of Mathematics Education and RINS, Gyeongsang National University, 501 Jinjudae-ro, Jinju, 660-701,
    South Korea
  • Department of Mathematics, Sungkyunkwan University, Suwon, 440-746, South Korea
Bibliografia
  • [1] A. O. L. Atkin and J. Lehner, Hecke operators on Г0(m), Math. Ann. 185 (1970), 134-160.
  • [2] R. E. Borcherds, Monstrous moonshine and monstrous Lie superalgebras, Invent. Math. 109 (1992), 405–444.
  • [3] D. Choi amd Y. Choie, p -adic limit of the Fourier coefficients of weakly holomorphic modular forms of half integral weight, Israel J.Math. 175 (2010), 61–83.
  • [4] D. Choi amd Y. Choie, Weight-dependent congruence properties of modular forms, J. Number Theory 122 (2007), no. 2, 301–313.[WoS]
  • [5] D. Choi amd Y. Choie, Linear relations among the Fourier coefficients of modular forms on groups Г0(N) of genus zero and theirapplications, J. Math. Anal. Appl. 326 (2007), no. 1, 655–666.[WoS]
  • [6] S. Choi and C. H. Kim, Congruences for Hecke eigenvalues in higher level cases, J. Number Theory 131 (2011), no. 11, 2023–2036.[WoS]
  • [7] S. Choi and C. H. Kim, Basis for the space of weakly holomorphic modular forms in higher level cases, J. Number Theory 133(2013), no. 4, 1300–1311.[WoS]
  • [8] Y. Choie, W. Kohnen and K Ono, Linear relations between modular form coefficients and non-ordinary primes, Bull. London Math.Soc. 37 (2005), no. 3, 335–341.
  • [9] J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. London Math. Soc. 11 (1979), 308–339.
  • [10] W. Duke and P. Jenkins, On the zeros and coefficients of certain weakly holomorphic modular forms, Pure Appl. Math. Q. 4(2008), 1327–1340.
  • [11] P. Guerzhoy, Hecke operators for weakly holomorphic modular forms and supersingular congruences, Proc. Amer. Math. Soc.136 (2008), 3051-3059.[WoS]
  • [12] K. Harada, Moonshine of finite groups, The Ohio State University Lecture Notes.
  • [13] N. Koblitz, Introduction to elliptic curves and modular forms, Springer-Verlag, New York, 1984.
  • [14] M. Koike, On replication formula and Hecke operators, Nogoya University, preprint.
  • [15] A. Krieg, Modular forms on the Fricke group, Abh. Math. Sem. Univ. Hamburg 65 (1995), 293-299.
  • [16] S. Lang, Introduction to modular forms, Grundlehren der mathematischen Wissenschaften, No. 222. Springer-Verlag, Berlin-NewYork, 1976.
  • [17] J. Lewis and D. Zagier, Periodic functions for Maass wave forms I, Ann. of Math. (2) 153 (2001), 191-258.
  • [18] T. Miyake, Modular forms, Springer, 1989.
  • [19] K. Ono, The web of modularity: Arithmetic of the coefficients of modular forms and q-series, volume 102 of CBMS regionalconference series in mathematics. American Mathematical Society, 2004.
  • [20] J. Shigezumi, On the zeros of the Eisenstein series for Г0(5) and Г0(7), Kyushu J. Math. 61 (2007), no. 2, 527-549.
  • [21] G. Shimura, Introduction to the arithmetic theory of automorphic forms, Princeton University Press, 1971.
  • [22] W. Stein, http://wstein.org.
  • [23] D. Zagier, Introduction to modular forms, From number theory to physics (Les Houches, 1989), 238-291, Springer, 1992.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_math-2015-0062
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