Class invariants and cyclotomic unit groups from special values of modular units
Amanda Folsom1
1 Department of Mathematics University of California, Los Angeles Box 951555 Los Angeles, CA 90095-1555, USA
Journal de théorie des nombres de Bordeaux, Volume 20 (2008) no. 2, pp. 289-325.

In this article we obtain class invariants and cyclotomic unit groups by considering specializations of modular units. We construct these modular units from functional solutions to higher order q-recurrence equations given by Selberg in his work generalizing the Rogers-Ramanujan identities. As a corollary, we provide a new proof of a result of Zagier and Gupta, originally considered by Gauss, regarding the Gauss periods. These results comprise part of the author’s 2006 Ph.D. thesis [6] in which the structure of these modular unit groups and their associated cuspidal divisor class groups are also characterized, and a cuspidal divisor class number formula is given in terms of products of L-functions and compared to the classical relative class number formula within the cyclotomic fields [6, 7].

Dans cet article, nous obtenons des invariants de classe et des groupes d’unités cyclotomiques en considérant des spécialisations d’unités modulaires. Nous construisons ces unités modulaires à partir de solutions d’équations fonctionnelles de q-récurrence données par Selberg dans son travail généralisant les identités de Rogers-Ramanujan. Commme corollaire, nous donnons une nouvelle preuve d’un résultat de Zagier et Gupta, originellement considéré par Gauss, à propos des périodes de Gauss. Ces résultats proviennent pour partie de la thèse de l’auteur en 2006 [6] dans laquelle la structure de ces groupes d’unités modulaires et de leur groupe de classes de diviseurs cuspidaux associé est donnée en termes de produits de fonctions L et comparée à la formule classique du nombre de classes relatives pour les corps cyclotomiques [6, 7].

DOI: 10.5802/jtnb.628
Amanda Folsom 1

1 Department of Mathematics University of California, Los Angeles Box 951555 Los Angeles, CA 90095-1555, USA 
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Amanda Folsom. Class invariants and cyclotomic unit groups from special values of modular units. Journal de théorie des nombres de Bordeaux, Volume 20 (2008) no. 2, pp. 289-325. doi : 10.5802/jtnb.628. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.628/

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