On a generalization of the rank one Rubin-Stark conjecture

DOI10.1016/J.JNT.2012.05.008zbMath1368.11117OpenAlexW2041082071WikidataQ123014690 ScholiaQ123014690MaRDI QIDQ452387

Daniel Vallières

Publication date: 21 September 2012

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2012.05.008

zbMATH Keywords

class groupsStark's conjectures

Mathematics Subject Classification ID

Class numbers, class groups, discriminants (11R29) Zeta functions and (L)-functions of number fields (11R42)

Related Items (4)

The equivariant Tamagawa number conjecture and the extended abelian Stark conjecture ⋮ The \((S, \{2 \})\)-Iwasawa theory ⋮ Numerical evidence for higher order Stark-type conjectures ⋮ On \(p\)-adic Diamond-Euler log gamma functions

Uses Software

• PARI/GP
• SageMath

Cites Work

• Two cases of Stark's conjecture
• The Stark conjectures on Artin \(L\)-functions at \(s=0\). Lecture notes of a course in Orsay edited by Dominique Bernardi and Norbert Schappacher.
• Special values of Abelian \(L\)-functions at \(s=0\)
• An extension of the first-order Stark conjecture
• Values of abelian \(L\)-functions at negative integers over totally real fields
• \(L\)-functions at \(s=1\). IV: First derivatives at \(s=0\)
• Values at negative integers of zeta functions and \(p\)-adic zeta functions
• A Stark conjecture ``over \({\mathbb{Z}}\) for abelian \(L\)-functions with multiple zeros
• Galois groups of exponent two and the Brumer-Stark conjecture.
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