论文标题
艾森斯坦零多项式序列的零多项式的不可约性
Irreducibility of the zero polynomials of Eisenstein series
论文作者
论文摘要
令$ e_k $为$ \ mathrm {sl} _ {2}（\ Mathbb {z}）$的标准化EISENSTEIN系列重量$ K $。令$φ_K$为编码$ e_k $的非elliptic zeros的$ j $ invariants的多项式。在2001年，Gekeler观察到多项式$φ_K$似乎是不可约的（并以$ k \ leq 446 $验证了这一主张）。我们表明$φ_K$对于无限的许多$ k $不可修复。
Let $E_k$ be the normalized Eisenstein series of weight $k$ on $\mathrm{SL}_{2}(\mathbb{Z})$. Let $φ_k$ be the polynomial that encodes the $j$-invariants of non-elliptic zeros of $E_k$. In 2001, Gekeler observed that the polynomials $φ_k$ seem to be irreducible (and verified this claim for $k\leq 446$). We show that $φ_k$ is irreducible for infinitely many $k$.
