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Mathematics of Computation

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Cyclotomic invariants and $ E$-irregular primes

Authors: R. Ernvall and T. Metsänkylä
Journal: Math. Comp. 32 (1978), 617-629
MSC: Primary 12A35; Secondary 10A40, 12A50
Corrigendum: Math. Comp. 33 (1979), 433.
Corrigendum: Math. Comp. 33 (1979), 432-433.
MathSciNet review: 482273
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Abstract: We prove some general results about the Iwasawa invariants $ {\lambda ^ - }$ and $ {\mu ^ - }$ of the 4pth cyclotomic field (p an odd prime), and determine the values of these invariants for $ p < {10^4}$. The properties of $ {\lambda ^ - }$ and $ {\mu ^ - }$ are closely connected with the E-irregularity (i.e. the irregularity with respect to the Euler numbers) of p. A list of all E-irregular primes less than $ {10^4}$, computed by the first author, is included and analyzed.

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Keywords: Class numbers, cyclotomic fields, $ {Z_p}$-extensions, E-irregular primes, irregular primes, Euler numbers, Fermat's Last Theorem, Fermat quotients
Article copyright: © Copyright 1978 American Mathematical Society