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arXiv · 1712.06502

Fields generated by sums and products of singular moduli

Bernadette Faye·Antonin Riffaut
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Abstract

We show that the field $\mathbb{Q}(x,y)$, generated by two singular moduli~$x$ and~$y$, is generated by their sum ${x+y}$, unless~$x$ and~$y$ are conjugate over~$\mathbb{Q}$, in which case ${x+y}$ generates a subfield of degree at most~$2$. We obtain a similar result for the product of two singular moduli.

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Bernadette Faye, Antonin Riffaut. 2017-12-15. Fields generated by sums and products of singular moduli. https://arxiv.org/abs/1712.06502

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