On the rank one abelian Gross-Stark conjecture

DOI10.4171/CMH/374zbMath1377.11113arXiv1308.2261WikidataQ122916618 ScholiaQ122916618MaRDI QIDQ906568

Kevin Ventullo

Publication date: 22 January 2016

Published in: Commentarii Mathematici Helvetici (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1308.2261

zbMATH Keywords

\(p\)-adic \(L\)-functionsIwasawa main conjectureHida familiesStark conjecture

Mathematics Subject Classification ID

Congruences for modular and (p)-adic modular forms (11F33) Galois representations (11F80) Iwasawa theory (11R23) Zeta functions and (L)-functions (11S40) Automorphic forms on (mbox{GL}(2)); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces (11F41)

Related Items (10)

On the Gross-Stark conjecture ⋮ On Iwasawa theory, zeta elements for \(\mathbb G_m\), and the equivariant Tamagawa number conjecture ⋮ On the minus component of the equivariant Tamagawa number conjecture for \(\mathbb{G}_m\) ⋮ The derivative formula of \(p\)-adic \(L\)-functions for imaginary quadratic fields at trivial zeros ⋮ 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 ⋮ Galois coinvariants of the unramified Iwasawa modules of multiple \(\mathbb{Z}_p\)-extensions ⋮ Level raising for \(p\)-adic Hilbert modular forms ⋮ Overconvergent generalised eigenforms of weight one and class fields of real quadratic fields ⋮ On the characteristic polynomial of the Gross regulator matrix

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