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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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Multiplicities of dihedral discriminants
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by Daniel C. Mayer PDF
Math. Comp. 58 (1992), 831-847 Request permission


Given the discriminant ${d_k}$ of a quadratic field k, the number of cyclic relative extensions $N|k$ of fixed odd prime degree p with dihedral absolute Galois group of order 2p, which share a common conductor f, is called the multiplicity of the dihedral discriminant ${d_N} = {f^{2(p - 1)}}d_k^p$. In this paper, general formulas for multiplicities of dihedral discriminants are derived by analyzing the p-rank of the ring class group mod f of k. For the special case $p = 3,{d_k} = - 3$, an elementary proof is given additionally. The theory is illustrated by a discussion of all known discriminants of multiplicity $\geq 5$ of totally real and complex cubic fields.
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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Math. Comp. 58 (1992), 831-847
  • MSC: Primary 11R29; Secondary 11R16, 11R20
  • DOI:
  • MathSciNet review: 1122071