A refinement of Stark's conjecture over complex cubic number fields

DOI10.1016/j.jnt.2008.10.015zbMath1184.11048OpenAlexW2049298916WikidataQ123289844 ScholiaQ123289844MaRDI QIDQ1011661

Robert Sczech, Tian Ren

Publication date: 9 April 2009

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2008.10.015

zbMATH Keywords

Shintani zeta functionclass field theoryShintani domainsunits of cubic number fields

Mathematics Subject Classification ID

Units and factorization (11R27) Class field theory (11R37) Zeta functions and (L)-functions of number fields (11R42)

Related Items (3)

On the theory of normalized Shintani \(L\)-functions and its application to Hecke \(L\)-functions. I. Real quadratic fields ⋮ Signed Shintani cones for number fields with one complex place ⋮ An enhancement of Zagier’s polylogarithm conjecture

Cites Work

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• The Stark conjectures on Artin \(L\)-functions at \(s=0\). Lecture notes of a course in Orsay edited by Dominique Bernardi and Norbert Schappacher.
• Shintani zeta functions and Gross-Stark units for totally real fields
• Arguments for the Stark units and periods of Eisenstein series
• Values of abelian \(L\)-functions at negative integers over totally real fields
• \(L\)-functions at \(s=1\). IV: First derivatives at \(s=0\)
• \(L\)-functions at \(s=1\). III: Totally real fields and Hilbert's twelfth problem
• Eisenstein group cocycles for \(\text{GL}_ n\) and values of \(L\)- functions
• Stark's conjecture over complex cubic number fields
• On Barnes' multiple zeta and gamma functions

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