Computation of -units in ray class fields of real quadratic number fields
Author:
Hugo Chapdelaine
Journal:
Math. Comp. 78 (2009), 2307-2345
MSC (2000):
Primary 11S31
DOI:
https://doi.org/10.1090/S0025-5718-09-02215-7
Published electronically:
January 29, 2009
MathSciNet review:
2521291
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: Let be a real quadratic field, let
be a prime number which is inert in
and let
be the completion of
at
. As part of a Ph.D. thesis, we constructed a certain
-adic invariant
, and conjectured that
is, in fact, a
-unit in a suitable narrow ray class field of
. In this paper we give numerical evidence in support of that conjecture. Our method of computation is similar to the one developed by Dasgupta and relies on partial modular symbols attached to Eisenstein series.
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-units in ray class fields of real quadratic number fields.
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Additional Information
Hugo Chapdelaine
Affiliation:
Département de Mathématiques et de Statistique, Université Laval, Québec, Canada G1K 7P4
Email:
hugo.chapdelaine@mat.ulaval.ca
DOI:
https://doi.org/10.1090/S0025-5718-09-02215-7
Keywords:
$p$-adic Gross-Stark conjectures,
explicit Class field theory,
$p$-adic integration,
Eisenstein series
Received by editor(s):
November 14, 2007
Received by editor(s) in revised form:
August 27, 2008
Published electronically:
January 29, 2009
Additional Notes:
The author is grateful to the Max Planck Institut für Mathematik for the financial support during the writing of the paper.
Article copyright:
© Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.