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Main Authors: Anderson, Gradin, Harrigan, Peter, Hoback, Louisa, Pugh, McKayah, Wong, Tian An
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2509.17256
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author Anderson, Gradin
Harrigan, Peter
Hoback, Louisa
Pugh, McKayah
Wong, Tian An
author_facet Anderson, Gradin
Harrigan, Peter
Hoback, Louisa
Pugh, McKayah
Wong, Tian An
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2509_17256
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Bianchi Modular Forms and the Rationality of Periods
Anderson, Gradin
Harrigan, Peter
Hoback, Louisa
Pugh, McKayah
Wong, Tian An
Number Theory
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.
title Bianchi Modular Forms and the Rationality of Periods
topic Number Theory
url https://arxiv.org/abs/2509.17256