Shintani zeta functions and Gross-Stark units for totally real fields

DOI10.1215/00127094-2008-019zbMath1235.11102OpenAlexW2073869955MaRDI QIDQ930134

Samit Dasgupta

Publication date: 20 June 2008

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/5e9c9b9b848dc95c431087454771b7fb11de9471

Mathematics Subject Classification ID

Class field theory (11R37) Zeta functions and (L)-functions of number fields (11R42) Totally real fields (11R80)

Related Items (14)

ANOTHER LOOK AT GROSS–STARK UNITS OVER THE NUMBER FIELD ℚ ⋮ A conjectural product formula for Brumer-Stark units over real quadratic fields ⋮ On the Brumer-Stark conjecture and refinements ⋮ Comparing two formulas for the Gross-Stark units ⋮ A note on the central limit theorems for dependent random variables ⋮ p-Adic measures associated with zeta values and p-adic log multiple gamma functions ⋮ On the ratios of Barnes' multiple gamma functions to the \(p\)-adic analogues ⋮ Shintani cocycles and the order of vanishing of \(p\)-adic Hecke \(L\)-series at \(s=0\) ⋮ Computation of 𝑝-units in ray class fields of real quadratic number fields ⋮ A refinement of Stark's conjecture over complex cubic number fields ⋮ p-units in ray class fields of real quadratic number fields ⋮ On the characteristic polynomial of the Gross regulator matrix ⋮ An enhancement of Zagier’s polylogarithm conjecture ⋮ Computing 𝑝-adic L-functions of totally real fields

Cites Work

• Arguments for the Stark units and periods of Eisenstein series
• Residue at \(s=1\) of \(p\)-adic zeta functions
• Values of abelian \(L\)-functions at negative integers over totally real fields
• Values at negative integers of zeta functions and \(p\)-adic zeta functions
• Elliptic units for real quadratic fields
• Values of \(L\)-functions at \(s=1\). I: \(L\)-functions for quadratic forms
• On absolute CM-periods, II
• Stark's conjecture over complex cubic number fields
• Computations of Elliptic Units for Real Quadratic Fields
• Integration on \({\mathcal H_p}\times\mathcal H\) and arithmetic applications.
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