ArticleOriginal scientific text

Title

On cyclotomic ℤ ₚ-extensions of real quadratic fields

Authors 1

Affiliations

  1. Department of Mathematics, School of Science and Engineering, Waseda University, 3-4-1, Okubo Shinjuku-Ku, Tokyo, 169 Japan

Keywords

Iwasawa invariants, real quadratic fields, unit groups, ambiguous ideal class groups

Bibliography

  1. J. Coates, p-adic L-functions and Iwasawa's theory, in: Algebraic Number Fields, Durham Symposium, 1975, A. Fröhlich (ed.), Academic Press, 1977, 269-353.
  2. L. Federer, P-adic L-functions, regulators, and Iwasawa modules, Ph.D. Thesis, Princeton University, 1982.
  3. B. Ferrero and L. C. Washington, The Iwasawa invariant μₚ vanishes for abelian number fields, Ann. of Math. 109 (1979), 377-395.
  4. T. Fukuda and K. Komatsu, On the λ invariants of ℤₚ-extensions of real quadratic fields, J. Number Theory 23 (1986), 238-242.
  5. T. Fukuda and K. Komatsu, On ℤₚ-extensions of real quadratic fields, J. Math. Soc. Japan 38 (1986), 95-102.
  6. T. Fukuda and H. Taya, The Iwasawa λ-invariants of ℤₚ-extensions of real quadratic fields, Acta Arith. 69 (1995), 277-292.
  7. T. Fukuda and H. Taya, Computational research on Greenberg's conjecture for real quadratic fields, Mem. School Sci. Engrg. Waseda Univ. Tokyo 58 (1994), 175-203.
  8. R. Greenberg, On the Iwasawa invariants of totally real number fields, Amer. J. Math. 98 (1976), 263-284.
  9. K. Iwasawa, On Γ-extensions of algebraic number fields, Bull. Amer. Math. Soc. 65 (1959), 183-226.
  10. K. Iwasawa, Lectures on p-Adic L-Functions, Ann. of Math. Stud. 74, Princeton Univ. Press, Princeton, N.J., 1972.
  11. H. Taya, On the Iwasawa λ-invariants of real quadratic fields, Tokyo J. Math. 16 (1993), 121-130.
  12. H. Taya, Computation of ℤ₃-invariants of real quadratic fields, Math. Comp., to appear.
  13. L. C. Washington, Introduction to Cyclotomic Fields, Graduate Texts in Math. 83, Springer, New York, 1982.
Pages:
107-119
Main language of publication
English
Received
1994-12-08
Accepted
1995-07-11
Published
1996
Exact and natural sciences