On the Stark-Shintani conjecture and cyclotomic Zp-extensions of class fields over real quadratic fields

Jin NAKAGAWA

doi:10.2969/jmsj/03640577

On the Stark-Shintani conjecture and cyclotomic Z_p-extensions of class fields over real quadratic fields

Jin NAKAGAWA

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1984 Volume 36 Issue 4 Pages 577-588

DOI https://doi.org/10.2969/jmsj/03640577

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Published: 1984 Received: July 29, 1983 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: AFFILIATION Details: Wrong :
1) Mathematical Institute Tohoku University

Right :
1) Mathematical Institute Tôhoku University

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) T. Arakawa, On the Stark-Shintani ray class invariants of real quadratic fields and certain relative class numbers, RIMS Kokuroku, 497 (1983), 116-138 (Japanese).
2) T. Chinburg, Stark's conjecture for L-functions with first-order zeroes at s=0, Advances in Math., 48 (1983), 82-113.
3) R. F. Coleman, Division values in local fields, Invent. Math., 53 (1979), 91-116.
4) N. Jacobson, Lectures in Abstract Algebra, III, Van Nostrand, New York, 1964.
5) T. Shintani, On certain ray class invariants of real quadratic fields, J. Math. Soc. Japan, 30 (1978), 139-167.
6) H. M. Stark, L-functions at s=1. II. Artin L-functions with rational characters, Advances in Math., 17 (1975), 60-92.
7) H. M. Stark, L-functions at s=1. III. Totally real fields and Hilbert's twelfth problem, Advances in Math., 22 (1976), 64-84.
8) H. M. Stark, Class fields for real quadratic fields and L-series at s=1, Proc. Durham Conf., Academic Press, New York, 1977, 355-374.
9) H. M. Stark, L-functions at s=1. IV. First derivatives at s=0, Advances in Math., 35 (1980), 197-235.
10) J. Tate, On Stark's conjectures on the behavior of L(s, χ) at s=0, J. Fac. Sci. Univ. Tokyo Sect. IA, 28 (1981), 963-978.

Right : [1] T. Arakawa, On the Stark-Shintani ray class invariants of real quadratic fields and certain relative class numbers, RIMS Kokuroku, 497 (1983), 116-138 (Japanese).
[2] T. Chinburg, Stark's conjecture for L-functions with first-order zeroes at s=0, Advances in Math., 48 (1983), 82-113.
[3] R. F. Coleman, Division values in local fields, Invent. Math., 53 (1979), 91-116.
[4] N. Jacobson, Lectures in Abstract Algebra, III, Van Nostrand, New York, 1964.
[5] T. Shintani, On certain ray class invariants of real quadratic fields, J. Math. Soc. Japan, 30 (1978), 139-167.
[6] H. M. Stark, L-functions at s=1. II. Artin L-functions with rational characters, Advances in Math., 17 (1975), 60-92.
[7] H. M. Stark, L-functions at s=1. III. Totally real fields and Hilbert's twelfth problem, Advances in Math., 22 (1976), 64-84.
[8] H. M. Stark, Class fields for real quadratic fields and L-series at s=1, Proc. Durham Conf., Academic Press, New York, 1977, 355-374.
[9] H. M. Stark, L-functions at s=1. IV. First derivatives at s=0, Advances in Math., 35 (1980), 197-235.
[10] J. Tate, On Stark's conjectures on the behavior of L(s, χ) at s=0, J. Fac. Sci. Univ. Tokyo Sect. IA, 28 (1981), 963-978.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

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