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Irregular prime divisors of the Bernoulli numbers. (English) Zbl 0293.10008


MSC:

11B68 Bernoulli and Euler numbers and polynomials
11R18 Cyclotomic extensions
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References:

[1] A. I. Borevich and I. R. Shafarevich, Number theory, Translated from the Russian by Newcomb Greenleaf. Pure and Applied Mathematics, Vol. 20, Academic Press, New York-London, 1966. · Zbl 0145.04902
[2] L. Carlitz, Note on irregular primes, Proc. Amer. Math. Soc. 5 (1954), 329 – 331. · Zbl 0058.03702
[3] Kenkichi Iwasawa, On some invariants of cyclotomic fields, Amer. J. Math. 80 (1958), 773-783; erratum 81 (1958), 280. · Zbl 0084.04101
[4] Kenkichi Iwasawa and Charles C. Sims, Computation of invariants in the theory of cyclotomic fields, J. Math. Soc. Japan 18 (1966), 86 – 96. · Zbl 0141.04901 · doi:10.2969/jmsj/01810086
[5] Wells Johnson, On the vanishing of the Iwasawa invariant \?_{\?} for \?<8000, Math. Comp. 27 (1973), 387 – 396. · Zbl 0281.12006
[6] Emma Lehmer, On congruences involving Bernoulli numbers and the quotients of Fermat and Wilson, Ann. of Math. (2) 39 (1938), no. 2, 350 – 360. · Zbl 0019.00505 · doi:10.2307/1968791
[7] Tauno Metsänkylä, Note on the distribution of irregular primes, Ann. Acad. Sci. Fenn. Ser. A I No. 492 (1971), 7. · Zbl 0208.05502
[8] Hugh L. Montgomery, Distribution of irregular primes, Illinois J. Math. 9 (1965), 553 – 558. · Zbl 0131.04501
[9] F. Pollaczek, Über die irregulären Kreiskörper der \?-ten und \?²-ten Einheitswurzeln, Math. Z. 21 (1924), no. 1, 1 – 38 (German). · JFM 50.0111.02 · doi:10.1007/BF01187449
[10] J. Uspensky & M. Heaslet, Elementary Number Theory, McGraw-Hill, New York, 1939. MR 1, 38. · Zbl 0022.30602
[11] H. S. Vandiver, ”Is there an infinity of regular primes?,” Scripta Math., v. 21, 1955, pp. 306-309. · Zbl 0071.04402
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