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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 number parity for the $p$th cyclotomic field
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by Peter Stevenhagen PDF
Math. Comp. 63 (1994), 773-784 Request permission

Abstract:

We study the parity of the class number of the pth cyclotomic field for p prime. By analytic methods we derive a parity criterion in terms of polynomials over the field of 2 elements. The conjecture that the class number is odd for p a prime of the form $2q + 1$, with q prime, is proved in special cases, and a heuristic argument is given in favor of the conjecture. An implementation of the criterion on a computer shows that no small counterexamples to the conjecture exist.
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Math. Comp. 63 (1994), 773-784
  • MSC: Primary 11R29; Secondary 11R18
  • DOI: https://doi.org/10.1090/S0025-5718-1994-1242060-X
  • MathSciNet review: 1242060