On cyclotomic ℤ ₚ-extensions of real quadratic fields

Hisao Taya

Acta Arithmetica (1996)

  • Volume: 74, Issue: 2, page 107-119
  • ISSN: 0065-1036

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Hisao Taya. "On cyclotomic ℤ ₚ-extensions of real quadratic fields." Acta Arithmetica 74.2 (1996): 107-119. <http://eudml.org/doc/206840>.

@article{HisaoTaya1996,
author = {Hisao Taya},
journal = {Acta Arithmetica},
keywords = {Iwasawa invariants; real quadratic fields; unit groups; ambiguous ideal class groups; cyclotomic extension; Iwasawa theory; real quadratic field; invariants; ambiguous class groups; Iwasawa -invariants},
language = {eng},
number = {2},
pages = {107-119},
title = {On cyclotomic ℤ ₚ-extensions of real quadratic fields},
url = {http://eudml.org/doc/206840},
volume = {74},
year = {1996},
}

TY - JOUR
AU - Hisao Taya
TI - On cyclotomic ℤ ₚ-extensions of real quadratic fields
JO - Acta Arithmetica
PY - 1996
VL - 74
IS - 2
SP - 107
EP - 119
LA - eng
KW - Iwasawa invariants; real quadratic fields; unit groups; ambiguous ideal class groups; cyclotomic extension; Iwasawa theory; real quadratic field; invariants; ambiguous class groups; Iwasawa -invariants
UR - http://eudml.org/doc/206840
ER -

References

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  1. [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. [2] L. Federer, P-adic L-functions, regulators, and Iwasawa modules, Ph.D. Thesis, Princeton University, 1982. Zbl0504.12009
  3. [3] B. Ferrero and L. C. Washington, The Iwasawa invariant μₚ vanishes for abelian number fields, Ann. of Math. 109 (1979), 377-395. Zbl0443.12001
  4. [4] T. Fukuda and K. Komatsu, On the λ invariants of ℤₚ-extensions of real quadratic fields, J. Number Theory 23 (1986), 238-242. Zbl0593.12003
  5. [5] T. Fukuda and K. Komatsu, On ℤₚ-extensions of real quadratic fields, J. Math. Soc. Japan 38 (1986), 95-102. Zbl0588.12004
  6. [6] T. Fukuda and H. Taya, The Iwasawa λ-invariants of ℤₚ-extensions of real quadratic fields, Acta Arith. 69 (1995), 277-292. Zbl0828.11060
  7. [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. Zbl0852.11064
  8. [8] R. Greenberg, On the Iwasawa invariants of totally real number fields, Amer. J. Math. 98 (1976), 263-284. Zbl0334.12013
  9. [9] K. Iwasawa, On Γ-extensions of algebraic number fields, Bull. Amer. Math. Soc. 65 (1959), 183-226. 
  10. [10] K. Iwasawa, Lectures on p-Adic L-Functions, Ann. of Math. Stud. 74, Princeton Univ. Press, Princeton, N.J., 1972. Zbl0236.12001
  11. [11] H. Taya, On the Iwasawa λ-invariants of real quadratic fields, Tokyo J. Math. 16 (1993), 121-130. Zbl0797.11084
  12. [12] H. Taya, Computation of ℤ₃-invariants of real quadratic fields, Math. Comp., to appear. Zbl0851.11062
  13. [13] L. C. Washington, Introduction to Cyclotomic Fields, Graduate Texts in Math. 83, Springer, New York, 1982. 

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