论文标题
Meromoromormormormormormormormormormormorphic模块形式的傅立叶系数的算术特性
Arithmetic properties of Fourier coefficients of meromorphic modular forms
论文作者
论文摘要
我们研究了与正相确定的积分二元二元形式相关的Meromormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormororig模块化形式的完整性和划分性能。例如，我们表明，如果没有非平凡的尖端形式的重量$ 2K $，则这些Meromorormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormorphic模块化表格的$ N^{K-1} $对于每个自然数量$ n $都可以排除。此外，我们证明它们的系数是不变的，并且具有恒定或交替的迹象。最后，我们获得了Meromormormormormormormormorphic模块化形式的傅立叶系数，$ J $功能的系数和分区函数之间的关系。
We investigate integrality and divisibility properties of Fourier coefficients of meromorphic modular forms of weight $2k$ associated to positive definite integral binary quadratic forms. For example, we show that if there are no non-trivial cusp forms of weight $2k$, then the $n$-th coefficients of these meromorphic modular forms are divisible by $n^{k-1}$ for every natural number $n$. Moreover, we prove that their coefficients are non-vanishing and have either constant or alternating signs. Finally, we obtain a relation between the Fourier coefficients of meromorphic modular forms, the coefficients of the $j$-function, and the partition function.
