On the vanishing of the Iwasawa invariant for
Author:
Wells Johnson
Journal:
Math. Comp. 27 (1973), 387396
MSC:
Primary 12A35; Secondary 10A40
MathSciNet review:
0384748
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Abstract 
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Abstract: The irregular primes less than 8000 are computed, and it is shown that the Iwasawa invariant for all primes .
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 [8a]
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H. Lehmer, Emma
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D. Mirimanoff, "Sur la congruence ," J. Reine Angew. Math., v. 115, 1895, pp. 295300.
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J. L. Selfridge & B. W. Pollack, "Fermat's last theorem is true for any exponent up to 25,000," Notices Amer. Math. Soc., v. 11, 1964, p. 97. Abstract #608138.
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J.P. Serre, Classes des corps cyclotomiques (d'après K. Iwasawa), Séminaire Bourbaki 1958/59, Exposé 174, fasc. 1, Secrétariat mathématique, Paris, 1959. MR 28 #1091.
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 Z. I. Borevič & I. R. Šafarevič, Number Theory, "Nauka," Moscow, 1964; English transl., Pure and Appl. Math., vol. 20, Academic Press, New York, 1966. MR 30 #1080; MR 33 #4001. MR 0195803 (33:4001)
 [2]
 L. Carlitz, "Problem 795," Math. Mag., v. 44, 1971, p. 106.
 [3]
 K. Iwasawa, "On some invariants of cyclotomic fields," Amer. J. Math., v. 80, 1958, pp. 773783; erratum, ibid., v. 81, 1959, p. 280. MR 23 #A1631. MR 0124317 (23:A1631)
 [4]
 K. Iwasawa, "On extensions of algebraic number fields," Bull. Amer. Math. Soc., v. 65, 1959, pp. 183226. MR 23 #A1630. MR 0124316 (23:A1630)
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 K. Iwasawa, "A class number formula for cyclotomic fields," Ann. of Math., (2), v. 76, 1962, pp. 171179. MR 27 #4806. MR 0154862 (27:4806)
 [6]
 K. Iwasawa, "On some modules in the theory of cyclotomic fields," J. Math. Soc. Japan, v. 16, 1964, pp. 4282. MR 35 #6646. MR 0215811 (35:6646)
 [7]
 K. Iwasawa & C. Sims, "Computation of invariants in the theory of cyclotomic fields," J. Math. Soc. Japan, v. 18, 1966, pp. 8696. MR 34 #2560. MR 0202700 (34:2560)
 [8a]
 D. H. Lehmer, E. Lehmer & H. S. Vandiver, "An application of highspeed computing to Fermat's last theorem," Proc. Nat. Acad. Sci. U.S.A., v. 40, 1954, pp. 2533. MR 15, 778. MR 0061128 (15:778f)
 [8b]
 H. S. Vandiver, "Examination of methods of attack on the second case of Fermat's last theorem," Proc. Nat. Acad. Sci. U.S.A., v. 40, 1954, pp. 732735. MR 16, 13. MR 0062758 (16:13f)
 [8c]
 J. L. Selfridge, C. A. Nicol & H. S. Vandiver, "Proof of Fermat's last theorem for all prime exponents less than 4002," Proc. Nat. Acad. Sci. U.S.A., v. 41, 1955, pp. 970973. MR 17, 348. MR 0072892 (17:348a)
 [9]
 D. Mirimanoff, "Sur la congruence ," J. Reine Angew. Math., v. 115, 1895, pp. 295300.
 [10]
 J. L. Selfridge & B. W. Pollack, "Fermat's last theorem is true for any exponent up to 25,000," Notices Amer. Math. Soc., v. 11, 1964, p. 97. Abstract #608138.
 [11]
 J.P. Serre, Classes des corps cyclotomiques (d'après K. Iwasawa), Séminaire Bourbaki 1958/59, Exposé 174, fasc. 1, Secrétariat mathématique, Paris, 1959. MR 28 #1091.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197303847485
PII:
S 00255718(1973)03847485
Keywords:
Cyclotomic fields,
class numbers,
irregular primes,
extensions,
cyclotomic invariants,
Fermat's Last Theorem
Article copyright:
© Copyright 1973 American Mathematical Society
