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arXiv · 1604.01514

Generators of Siegel modular function field of higher genus and level

Ja Kyung Koo·Dong Hwa Shin·Dong Sung Yoon
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Abstract

For positive integers $g$ and $N$, let $\mathcal{F}_N$ be the field of meromorphic Siegel modular functions of genus $g$ and level $N$ whose Fourier coefficients belong to the $N$th cyclotomic field. We present explicit generators of $\mathcal{F}_N$ over $\mathcal{F}_1$ in terms of quotient of theta constants, when $g\geq2$ and $N\geq 3$.

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Ja Kyung Koo, Dong Hwa Shin, Dong Sung Yoon. 2016-04-06. Generators of Siegel modular function field of higher genus and level. https://arxiv.org/abs/1604.01514

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