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arXiv · 2203.11302

Irreducibility of the zero polynomials of Eisenstein series

Oscar E. González
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Abstract

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 $k$.

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Oscar E. González. 2022-03-21. Irreducibility of the zero polynomials of Eisenstein series. https://arxiv.org/abs/2203.11302

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