二级同余子群\(\Gamma_0(2)\)的弱全纯模形式的非平凡素数与同余式
Non-ordinary primes and congruences for weakly holomorphic modular forms of level 2
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中文总结 AI 辅助
研究\(\Gamma_0(2)\)的权为\(k\)且仅在尖点\(\infty\)有极点的弱全纯模形式傅里叶系数算术性质，利用典范基结构等，证明模\(p\geq5\)同余式族并推导推论。
中文摘要 AI 辅助
本文研究了对于同余子群\(\Gamma_0(2)\)，权为\(k\)且仅在尖点\(\infty\)处有极点的弱全纯模形式的傅里叶系数的算术性质。利用典范基的结构以及仅在\(\infty\)处有极点的弱全纯模形式空间系数之间的显式对偶性，我们证明了模素数\(p\geq5\)的一般同余式族，并推导了几个推论作为该定理应用的例子。
英文摘要
In this paper, we investigate the arithmetic properties of the Fourier coefficients of weakly holomorphic modular forms of weight $k$ for the congruence subgroup $Γ_0(2)$, which have poles exclusively at the cusp $\infty$. Using the structure of canonical bases and the explicit duality between the coefficients of spaces of weakly holomorphic modular forms, which have a pole only at $\infty$, we prove a general family of congruences modulo primes $p \ge 5$ and derive several corollaries as examples of the theorem's application.
