Shintani cocycles and the order of vanishing of \(p\)-adic Hecke \(L\)-series at \(s=0\)

DOI10.1007/s00208-013-0983-5zbMath1307.11125arXiv1203.6689OpenAlexW1972252866MaRDI QIDQ2249463

Michael Spiess

Publication date: 1 July 2014

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1203.6689

zbMATH Keywords

\(p\)-adic \(L\)-seriesHecke characterstotally real fields

Mathematics Subject Classification ID

Iwasawa theory (11R23) Zeta functions and (L)-functions (11S40) Totally real fields (11R80)

Related Items (15)

On the Gross-Stark conjecture ⋮ The Eisenstein cocycle and Gross's tower of fields conjecture ⋮ Topological polylogarithms and \(p\)-adic interpolation of \(L\)-values of totally real fields ⋮ On Iwasawa theory, zeta elements for \(\mathbb G_m\), and the equivariant Tamagawa number conjecture ⋮ On derivatives of \(p\)-adic \(L\)-series at \(s = 0\) ⋮ Canonical equivariant cohomology classes generating zeta values of totally real fields ⋮ On the Brumer-Stark conjecture and refinements ⋮ Ranks of matrices of logarithms of algebraic numbers. I: The theorems of Baker and Waldschmidt-Masser ⋮ Comparing two formulas for the Gross-Stark units ⋮ On special zeros of \(p\)-adic \(L\)-functions of Hilbert modular forms ⋮ Derivative at \(s = 1\) of the \(p\)-adic \(L\)-function of the symmetric square of a Hilbert modular form ⋮ On the characteristic polynomial of the Gross regulator matrix ⋮ On two conjectures of Gross for large vanishing orders ⋮ Conjectures of Brumer, Gross and Stark ⋮ \(p\)-adic polylogarithms and \(p\)-adic Hecke \(L\)-functions for totally real fields

Cites Work

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• Values at negative integers of zeta functions and \(p\)-adic zeta functions
• On special zeros of \(p\)-adic \(L\)-functions of Hilbert modular forms
• Integral Eisenstein cocycles on \(\mathrm{GL}_n\). I: Sczech's cocycle and \(p\)-adic \(L\)-functions of totally real fields
• The Iwasawa conjecture for totally real fields
• Properties of Higher-Dimensional Shintani Generating Functions and Cocycles on Pgl₃ (Q)
• Shintani cocycles on GL _n

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