On cyclotomic ℤ ₚ-extensions of real quadratic fields

• Autorzy: Hisao Taya
• Języki publikacji: EN

Słowa kluczowe

EN

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

Kategorie tematyczne

• 11R11: Quadratic extensions
• 11R23: Iwasawa theory
• 11R29: Class numbers, class groups, discriminants
• 11R27: Units and factorization

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1996
• Tom: 74
• Numer: 2
• Strony: 107-119

Daty

wydano

1996

otrzymano

1994-12-08

poprawiono

1995-07-11

Twórcy

autor

Hisao Taya

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

Bibliografia

• [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.