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This is a Quantitative Study study.

October 3, 2025Open Access

Bianchi Modular Forms and the Rationality of Periods

Puntos clave

Establishing an analogue of Manin's rationality theorem for bianchi periods is a major finding.
Using explicit proofs with bianchi period polynomials, a significant result of Hida is reaffirmed in a new way.
The study employs an Eichler-Shimura-Harder isomorphism for the analysis of bianchi cusp forms.
The action of Hecke operators in this context offers new insights into modular forms and their properties.

Resumen

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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Cite This Study

Anderson et al. (Sun,) studied this question.

synapsesocial.com/papers/68e040f7a99c246f578b3d57 https://doi.org/https://doi.org/10.48550/arxiv.2509.17256

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