A Dedekind–Rademacher cocycle for Bianchi groups
Kim Klinger-Logan1 ; Kalani Thalagoda2 ; Tian An Wong3
1 Kansas State University 1228 N Martin Luther King Jr Dr, 138 Cardwell Hall Manhattan, KS 66506, USA
2 Tulane University 6823 St. Charles Avenue New Orleans, LA 70118, USA
3 University of Michigan-Dearborn 4901 Evergreen Rd, 2002 CASL Building Dearborn, MI 48128, USA
Journal de théorie des nombres de Bordeaux, Tome 37 (2025) no. 1, pp. 285-298

We construct a generalization of the Dedekind–Rademacher cocycle to congruence subgroups of $\mathrm{SL}_2(\mathbb{C})$, and derive some of its basic properties. In particular, we show that it parametrizes a family of $L$-values and prove the integrality of these values.

Nous construisons un cocycle de Dedekind et Rademacher généralisé pour les sous-groupes de congruence de $\mathrm{SL}_2(\mathbb{C})$ et déduisons certaines de ses propriétés de base. En particulier, nous montrons qu’il paramétrise une famille de valeurs d’une certaine fonction $L$ et prouvons l’intégralité de ces valeurs.

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DOI : 10.5802/jtnb.1321
Classification : 11F20, 11F37
Keywords: Elliptic Dedekind sum, Bianchi modular forms, Dedekind–Rademacher cocycle

Kim Klinger-Logan 1 ; Kalani Thalagoda 2 ; Tian An Wong 3

1 Kansas State University 1228 N Martin Luther King Jr Dr, 138 Cardwell Hall Manhattan, KS 66506, USA
2 Tulane University 6823 St. Charles Avenue New Orleans, LA 70118, USA
3 University of Michigan-Dearborn 4901 Evergreen Rd, 2002 CASL Building Dearborn, MI 48128, USA
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {A {Dedekind{\textendash}Rademacher} cocycle for {Bianchi} groups},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
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Kim Klinger-Logan; Kalani Thalagoda; Tian An Wong. A Dedekind–Rademacher cocycle for Bianchi groups. Journal de théorie des nombres de Bordeaux, Tome 37 (2025) no. 1, pp. 285-298. doi: 10.5802/jtnb.1321

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