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This paper is motivated by a 2001 paper of Choie and Kim and a 2006 paper of Bump and Choie. The paper of Choie and Kim extends an earlier result of Bol for elliptic modular forms to the setting of Siegel and Jacobi forms. The paper of Bump and Choie provides a representation theoretic interpretation of the phenomenon, and shows how a natural generalization of Choie and Kim's result on Siegel modular forms follows from a natural conjecture regarding (g,K)-modules. In this paper, it is shown that the conjecture of Bump and Choie follows from work of Boe. A second proof which is along the lines of the proof given by Bump and Choie in the genus 2 case is also included, as is a similar treatment of the result of Choie and Kim on Jacobi forms.
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참고문헌 (9)
참고문헌 신청
B. D. Boe / 1982 / Homomorphisms between generalized Verma modules / 박사 / Yale University
B. D. Boe / 1985 / Homomorphisms between generalized Verma modules / Trans. Amer. Math. Soc 288 (2) : 791 ~ 799
D. Bump / 1997 / Automorphic Forms and Representations, Cambridge Studies in Advanced Mathematics, 55 / Cambridge University Press
D. Bump / 2006 / Derivatives of modular forms of negative weight / Pure Appl. Math. Q 2 (1) : 111 ~ 133
G. Bol / 1949 / Invarianten linearer differential gleichungen / Abh. Math. Sem. Univ. Hamburg 16 (3) : 1 ~ 28
B. D. Boe / 1985 / Homomorphisms between generalized Verma modules / Trans. Amer. Math. Soc 288 (2) : 791 ~ 799
D. Bump / 1997 / Automorphic Forms and Representations, Cambridge Studies in Advanced Mathematics, 55 / Cambridge University Press
D. Bump / 2006 / Derivatives of modular forms of negative weight / Pure Appl. Math. Q 2 (1) : 111 ~ 133
G. Bol / 1949 / Invarianten linearer differential gleichungen / Abh. Math. Sem. Univ. Hamburg 16 (3) : 1 ~ 28
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