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p-units in ray class fields of real quadratic number fields

Part of: Zeta and $L$-functions: analytic theory Algebraic number theory: local and $p$-adic fields

Published online by Cambridge University Press:  01 March 2009

Hugo Chapdelaine
Hugo Chapdelaine*
Affiliation:
Département de mathématiques et de statistique (DMS), Université Laval, Pavillon Alexandre-Vachon, 1045 avenue de la Médecine, Local 1056, Québec G1V 0A6, Canada (email: hugo.chapdelaine@mat.ulaval.ca)
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Abstract

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Let K be a real quadratic number field and let p be a prime number which is inert in K. We denote the completion of K at the place p by Kp. We propose a p-adic construction of special elements in Kp× and formulate the conjecture that they should be p-units lying in narrow ray class fields of K. The truth of this conjecture would entail an explicit class field theory for real quadratic number fields. This construction can be viewed as a natural generalization of a construction obtained by Darmon and Dasgupta who proposed a p-adic construction of p-units lying in narrow ring class fields of K.

Keywords

p-adic Gross–Stark conjecturesexplicit class field theoryp-adic integrationEisenstein series

MSC classification

Secondary: 11S40: Zeta functions and $L$-functions 11M99: None of the above, but in this section
Type
Research Article
Information
Compositio Mathematica , Volume 145 , Issue 2 , March 2009 , pp. 364 - 392
Copyright
Copyright © Foundation Compositio Mathematica 2009

References

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