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Class number parity for the $ p$th cyclotomic field

Author: Peter Stevenhagen
Journal: Math. Comp. 63 (1994), 773-784
MSC: Primary 11R29; Secondary 11R18
MathSciNet review: 1242060
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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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Article copyright: © Copyright 1994 American Mathematical Society

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