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arXiv · 2607.13536

Bernoulli determinants and cuspidal subgroups

François Brunault
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Abstract

We give an explicit formula for the order of the rational cuspidal class group of the modular curve $X_1(N)$ for an arbitrary integer $N$. The proof relies on results of Streng on the group of modular units on $X_1(N)$, and requires computing a certain determinant involving the second Bernoulli polynomial. We also define a higher weight analogue of the cuspidal class group and speculate that its order is related to a similar determinant defined using a higher degree Bernoulli polynomial.

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François Brunault. 2026-07-15. Bernoulli determinants and cuspidal subgroups. https://arxiv.org/abs/2607.13536

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