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

Abstract

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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].

How to cite

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Folsom, 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 -

References

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