Fourier coefficients of Hilbert modular forms at cusps

Tim Davis

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arXiv · 2203.14096

Fourier coefficients of Hilbert modular forms at cusps

Tim Davis

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Abstract

The aim of this article is to study the fields generated by the Fourier coefficients of Hilbert newforms at arbitrary cusps. Precisely, given a cuspidal Hilbert newform $f$ and a matrix $\sigma$ in (a suitable conjugate of) the Hilbert modular group, we give a cyclotomic extension of the field generated by the Fourier coefficients at infinity which contains all the Fourier coefficients of $f||_k\sigma$.

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Tim Davis. 2022-03-26. Fourier coefficients of Hilbert modular forms at cusps. https://arxiv.org/abs/2203.14096

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