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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 their applications, 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-New York, 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 regional conference 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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