Mathematics of Computation

Zeros of 2-adic

-functions and congruences for class numbers and fundamental units

Author(s): Daniel C. Shanks; Patrick J. Sime; Lawrence C. Washington.
Journal: Math. Comp. 68 (1999), 1243-1255.
MSC (1991): Primary 11R11; Secondary 11S40
Posted: February 10, 1999
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Abstract: We study the imaginary quadratic fields such that the Iwasawa $\lambda _{2}$ -invariant equals 1, obtaining information on zeros of

-adic

-functions and relating this to congruences for fundamental units and class numbers.

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Daniel C. Shanks
Affiliation: Department of Mathematics, University of Maryland, College Park, MD 20742

Patrick J. Sime
Affiliation: Department of Mathematics & Comp. Sci., Caldwell College, Caldwell, NJ 07006
Email: PSime@caldwell.edu

Lawrence C. Washington
Affiliation: Department of Mathematics, University of Maryland, College Park, MD 20742
Email: lcw@math.umd.edu

DOI: 10.1090/S0025-5718-99-01046-7
PII: S 0025-5718(99)01046-7
Keywords: Quadratic fields, $p$-adic $L$-functions
Received by editor(s): October 14, 1997
Posted: February 10, 1999
Additional Notes: The third author was partially supported by a grant from NSA, and also thanks the Institute for Advanced Study for its hospitality during part of the preparation of this paper.
Copyright of article: Copyright 1999, American Mathematical Society

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