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arXiv · 2306.14889

Igusa's map on modular forms vanishing on the hyperelliptic locus

J Bernatska·Y Kopeliovich
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Abstract

We extend Igusa's map $\rho$ to modular forms which vanish on the hyperelliptic locus of the Siegel upper half-plane. The lowest non-vanishing derivatives of such modular forms are computed with the help of the general Thomae formula, they serve as vector-valued modular forms. This approach is illustrated by examples in genera $3$ and $4$.

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J Bernatska, Y Kopeliovich. 2023-06-26. Igusa's map on modular forms vanishing on the hyperelliptic locus. https://arxiv.org/abs/2306.14889

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