This paper gives a new identification for Siegel modular forms with respect to any congru-ence subgroup by investigating the properties of their Fourier-Jacobi expansions, and verifies a com-parison theorem for the di...This paper gives a new identification for Siegel modular forms with respect to any congru-ence subgroup by investigating the properties of their Fourier-Jacobi expansions, and verifies a com-parison theorem for the dimensions of the spaces Snk(n) and Jk,10(n) with small weight k. These results can be used to estimate the dimension of the space of modular forms.展开更多
This paper verifies the singularity conjecture for Jacobi forms with higher degree in some typical cases, and gives constructions for the Jacobi cusp forms whose Fourier coefficients can be expressed by some kind of R...This paper verifies the singularity conjecture for Jacobi forms with higher degree in some typical cases, and gives constructions for the Jacobi cusp forms whose Fourier coefficients can be expressed by some kind of Rankin-type L-series.展开更多
For every Jacobi form of Shimura type over H × C, a system of L-functions associated to it is given. These L-functions can be analytically continued to the whole complex plane and satisfy a kind of functional equ...For every Jacobi form of Shimura type over H × C, a system of L-functions associated to it is given. These L-functions can be analytically continued to the whole complex plane and satisfy a kind of functional equation. As a consequence, Hecke's inverse theorem on modular forms is extended to the context of Jacobi forms with Shimura type.展开更多
文摘This paper gives a new identification for Siegel modular forms with respect to any congru-ence subgroup by investigating the properties of their Fourier-Jacobi expansions, and verifies a com-parison theorem for the dimensions of the spaces Snk(n) and Jk,10(n) with small weight k. These results can be used to estimate the dimension of the space of modular forms.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 19871013).
文摘This paper verifies the singularity conjecture for Jacobi forms with higher degree in some typical cases, and gives constructions for the Jacobi cusp forms whose Fourier coefficients can be expressed by some kind of Rankin-type L-series.
基金The author would like to thank the Mathematical Department of the University of Hong Kong, where this paper was finished, for its hospitality. This work was supported by the National Natural Science Foundation of China (Grant No.19871013).
文摘For every Jacobi form of Shimura type over H × C, a system of L-functions associated to it is given. These L-functions can be analytically continued to the whole complex plane and satisfy a kind of functional equation. As a consequence, Hecke's inverse theorem on modular forms is extended to the context of Jacobi forms with Shimura type.
