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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
DOI: https://doi.org/10.1090/S0025-5718-1978-0482273-9
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, <IMG WIDTH="29" HEIGHT="38" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="${Z_p}$">-extensions, <I>E</I>-irregular primes, irregular primes, Euler numbers, Fermat’s Last Theorem, Fermat quotients
Article copyright: © Copyright 1978 American Mathematical Society