\(p\)-adic Abelian Stark conjectures at \(s=1\)

DOI10.5802/aif.1891zbMath1039.11081OpenAlexW2122408208WikidataQ123097601 ScholiaQ123097601MaRDI QIDQ1613949

David R. Solomon

Publication date: 3 September 2002

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_2002__52_2_379_0

zbMATH Keywords

zeta-functionregular\(p\)-adic \(L\)-functionspecial valueunitS-unitabelian extensiontotally real fieldStark conjecture

Mathematics Subject Classification ID

Zeta functions and (L)-functions of number fields (11R42) Integral representations related to algebraic numbers; Galois module structure of rings of integers (11R33) Zeta functions and (L)-functions (11S40)

Related Items (7)

VALUES AT s = -1 OF L-FUNCTIONS FOR MULTI-QUADRATIC EXTENSIONS OF NUMBER FIELDS, AND THE FITTING IDEAL OF THE TAME KERNEL ⋮ A $p$-adic Stark conjecture in the rank one setting ⋮ On the p‐adic Stark conjecture at s=1 and applications ⋮ On twisted zeta-functions at \(s=0\) and partial zeta-functions at \(s=1\) ⋮ Testing the congruence conjecture for Rubin-Stark elements ⋮ Stark units and the main conjectures for totally real fields ⋮ Verifying a \(p\)-adic abelian Stark conjecture at \(s=1\).

Cites Work

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• The refined \(\mathfrak p\)-adic abelian Stark conjecture in function fields
• \(L\)-functions at \(s=1\). IV: First derivatives at \(s=0\)
• Another look at \(p\)-adic \(L\)-functions for totally real fields
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• Values at negative integers of zeta functions and \(p\)-adic zeta functions
• Galois relations for cyclotomic numbers and \(p\)-units
• Twisted zeta-functions and Abelian Stark conjectures
• A Stark conjecture ``over \({\mathbb{Z}}\) for abelian \(L\)-functions with multiple zeros
• Values of \(L\)-functions at \(s=1\). I: \(L\)-functions for quadratic forms
• Base change for Stark-type conjectures "over \mathbb{Z}"
• Fonctions zeta p-adiques des corps de nombres abeliens réels

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