On the Stark-Shintani conjecture and cyclotomic \({\mathbb{Z}}_ p\)-extensions of class fields over real quadratic fields

DOI10.2969/jmsj/03640577zbMath0549.12008OpenAlexW2153449356WikidataQ123123699 ScholiaQ123123699MaRDI QIDQ800420

Jin Nakagawa

Publication date: 1984

Published in: Journal of the Mathematical Society of Japan (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2969/jmsj/03640577

zbMATH Keywords

unitspartial zeta functionreal quadratic fieldcyclotomic \({\mathbb{Z}}_ p\)-extensionray-class fieldStark- Shintani conjecturesStark- Shintani invariant

Mathematics Subject Classification ID

Quadratic extensions (11R11) Units and factorization (11R27) (zeta (s)) and (L(s, chi)) (11M06) Zeta functions and (L)-functions of number fields (11R42) Cyclotomic extensions (11R18)

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Stark's conjecture and Abelian \(L\)-functions with higher order zeros at \(s=0\) ⋮ On the Stark-Shintani conjecture and cyclotomic \({\mathbb{Z}}_ p\)-extensions of class fields over real quadratic fields. II