Zeros of 2-adic 
-functions and congruences
for class numbers and fundamental units
Authors:
Daniel C. Shanks, Patrick J. Sime and Lawrence C. Washington
Journal:
Math. Comp. 68 (1999), 1243-1255
MSC (1991):
Primary 11R11; Secondary 11S40
DOI:
https://doi.org/10.1090/S0025-5718-99-01046-7
Published electronically:
February 10, 1999
MathSciNet review:
1622093
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We study the imaginary quadratic fields such that the Iwasawa 
-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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-adic 
-functions, Acta Arith. 48 (1987), 63-71. 
-extension of imaginary quadratic fields, Amer. J. Math. 102 (1980), 447-459. 
-extensions of imaginary quadratic fields, Tôhoku Math. J. (2), 31 (1979), 91-96. Retrieve articles in Mathematics of Computation of the American Mathematical Society with MSC (1991): 11R11, 11S40
Retrieve articles in all journals with MSC (1991): 11R11, 11S40
Additional Information
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:
https://doi.org/10.1090/S0025-5718-99-01046-7
Keywords:
Quadratic fields,
$p$-adic $L$-functions
Received by editor(s):
October 14, 1997
Published electronically:
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.
Article copyright:
© Copyright 1999
American Mathematical Society