참고문헌
- M. Eichler, The basis problem for modular forms and the traces of Hecke operators. Springer-Verlag, Lecture Notes in Math., Vol.320, pp. 75-151, 1972.
-
R. Godement, Les fonctions
${\zeta}$ des algebras simples I, II, Seminaire Bourbaki, 1958/1959. -
H. Hijikata, A. Pizer, T. Shemanske, The basis problem for modular forms on
${\Gamma}_0(N)$ Memoirs AMS, Vol.32 No.418, November, 1989. - S. Jun, The equalities between Brandt matrices on primitive orders, preprint.
-
S. Jun, On the representatives of modular forms on
${\Gamma}_0(N)$ , J. Algebra, Vol.64, pp. 340-390, 1980. https://doi.org/10.1016/0021-8693(80)90151-9 - A. Pizer, An algorithm for computing modular forms by theta series, J. KMS, Vol.34 No.4, pp. 808-816, 1997.
- H. Shimizu, On the traces of Hecke operators, J. Fac. Sci. Univ. Tokyo, Vol.10, pp. 1-19, 1963.
- H. Shimizu, On zeta functions of quaternion algebra, Ann. of Math., Vol.81, pp. 166-193, 1965. https://doi.org/10.2307/1970389
- G. Shimura, "Introduction to the arithmetic theory of automorphic functions", Princeton Univ Press, Princeton, N.J., 1971.
-
T. Tamagawa, On
${\zeta}$ functions of a division algebra, Ann. of Math. Vol.77, pp. 387-405, 1963. https://doi.org/10.2307/1970221