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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Class numbers of ray class fields of imaginary quadratic fields
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by Omer Kucuksakalli PDF
Math. Comp. 80 (2011), 1099-1122 Request permission


Let $K$ be an imaginary quadratic field with class number one and let $\mathfrak {p} \subset \mathcal {O}_K$ be a degree one prime ideal of norm $p$ not dividing $6d_K$. In this paper we generalize an algorithm of Schoof to compute the class numbers of ray class fields $K_{\mathfrak {p}}$ heuristically. We achieve this by using elliptic units analytically constructed by Stark and the Galois action on them given by Shimura’s reciprocity law. We have discovered a very interesting phenomenon where $p$ divides the class number of $K_{\mathfrak {p}}$. This is a counterexample to the elliptic analogue of Vandiver’s conjecture.
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Additional Information
  • Omer Kucuksakalli
  • Affiliation: University of Massachusetts, Amherst, Department of Mathematics and Statistics, Amherst, Massachusetts 01003
  • Address at time of publication: Middle East Technical University, Department of Mathematics, 06531 Ankara, Turkey
  • Email:
  • Received by editor(s): May 14, 2009
  • Received by editor(s) in revised form: January 1, 2010
  • Published electronically: September 2, 2010
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 80 (2011), 1099-1122
  • MSC (2010): Primary 11Y40
  • DOI:
  • MathSciNet review: 2772114