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arXiv · 2509.17256

Bianchi Modular Forms and the Rationality of Periods

Gradin Anderson·Peter Harrigan·Louisa Hoback·McKayah Pugh·Tian An Wong
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Abstract

Using an explicit Eichler-Shimura-Harder isomorphism, we establish the analogue of Manin's rationality theorem for Bianchi periods and hence special values of $L$-functions of Bianchi cusp forms. This gives a new short proof of a result of Hida in the case of Euclidean imaginary quadratic fields. In particular, we give an explicit proof using the space of Bianchi period polynomials constructed by Karabulut and describe the action of Hecke operators.

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Gradin Anderson, Peter Harrigan, Louisa Hoback, McKayah Pugh, Tian An Wong. 2025-09-21. Bianchi Modular Forms and the Rationality of Periods. https://arxiv.org/abs/2509.17256

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