# Class invariants and cyclotomic unit groups from special values of modular units

Amanda Folsom^{[1]}

- [1] Department of Mathematics University of California, Los Angeles Box 951555 Los Angeles, CA 90095-1555, USA

Journal de Théorie des Nombres de Bordeaux (2008)

- Volume: 20, Issue: 2, page 289-325
- ISSN: 1246-7405

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topFolsom, Amanda. "Class invariants and cyclotomic unit groups from special values of modular units." Journal de Théorie des Nombres de Bordeaux 20.2 (2008): 289-325. <http://eudml.org/doc/10837>.

@article{Folsom2008,

abstract = {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].},

affiliation = {Department of Mathematics University of California, Los Angeles Box 951555 Los Angeles, CA 90095-1555, USA},

author = {Folsom, Amanda},

journal = {Journal de Théorie des Nombres de Bordeaux},

keywords = {modular unit; class invariant; cyclotomic unit},

language = {eng},

number = {2},

pages = {289-325},

publisher = {Université Bordeaux 1},

title = {Class invariants and cyclotomic unit groups from special values of modular units},

url = {http://eudml.org/doc/10837},

volume = {20},

year = {2008},

}

TY - JOUR

AU - Folsom, Amanda

TI - Class invariants and cyclotomic unit groups from special values of modular units

JO - Journal de Théorie des Nombres de Bordeaux

PY - 2008

PB - Université Bordeaux 1

VL - 20

IS - 2

SP - 289

EP - 325

AB - 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].

LA - eng

KW - modular unit; class invariant; cyclotomic unit

UR - http://eudml.org/doc/10837

ER -

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