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
Modular forms with weight of r（≥2） were studied in many articles. But for the case of r≤2, there are a large number of fundamental problems which need to be studied. One of these is the existence of Poincare serie...Modular forms with weight of r（≥2） were studied in many articles. But for the case of r≤2, there are a large number of fundamental problems which need to be studied. One of these is the existence of Poincare series. As well known, for the full modular group Г=SL<sub>2</sub>（Z） and r】2, we can define the classical Poincare series P<sub>n</sub>（Z）展开更多
Let λsym2f(n) be the n-th coefficient in the Dirichlet series of the symmetric square L-function associated with a holomorphic primitive cusp form f.We prove Ω± results for λsym2f(n) and evaluate the number of...Let λsym2f(n) be the n-th coefficient in the Dirichlet series of the symmetric square L-function associated with a holomorphic primitive cusp form f.We prove Ω± results for λsym2f(n) and evaluate the number of positive(resp.,negative) λsym2f(n) in some intervals.展开更多
The so_called Jacobi_Eisenstein series is defined by E k, S (z, w)=∑y∈J ∞\J (1, j) Z 1|k, Sy(z, w) . The Fourier coefficients of E k, S is determined completely. The theorem extends the results of Eichler and Zagie...The so_called Jacobi_Eisenstein series is defined by E k, S (z, w)=∑y∈J ∞\J (1, j) Z 1|k, Sy(z, w) . The Fourier coefficients of E k, S is determined completely. The theorem extends the results of Eichler and Zagier to the case of general index matrices.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.
文摘Modular forms with weight of r（≥2） were studied in many articles. But for the case of r≤2, there are a large number of fundamental problems which need to be studied. One of these is the existence of Poincare series. As well known, for the full modular group Г=SL<sub>2</sub>（Z） and r】2, we can define the classical Poincare series P<sub>n</sub>（Z）
基金the James D.Wolfensohn Fundthe S.S.Chern Fund+1 种基金the Minerva Research FoundationNational Natural Science Foundation of China (Grant No.10531060) for their supports during the academicyear
文摘Let λsym2f(n) be the n-th coefficient in the Dirichlet series of the symmetric square L-function associated with a holomorphic primitive cusp form f.We prove Ω± results for λsym2f(n) and evaluate the number of positive(resp.,negative) λsym2f(n) in some intervals.
文摘The so_called Jacobi_Eisenstein series is defined by E k, S (z, w)=∑y∈J ∞\J (1, j) Z 1|k, Sy(z, w) . The Fourier coefficients of E k, S is determined completely. The theorem extends the results of Eichler and Zagier to the case of general index matrices.
