Congruences between derivatives of abelian \(L\)-functions at \(s =0\)

DOI10.1007/s00222-007-0052-3zbMath1133.11063OpenAlexW2003291619MaRDI QIDQ2385046

David J. Burns

Publication date: 11 October 2007

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00222-007-0052-3

zbMATH Keywords

\(L\)-functionsglobal fieldsrefined abelian Stark conjectureRubin-Stark units

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) Galois cohomology (11R34)

Related Items (25)

Extremely strong boundary points and real-linear isometries ⋮ Refined class number formulas for \(\mathbb{G}_m\) ⋮ On the equivariant Tamagawa number conjecture for \(A_4\)-extensions of number fields ⋮ On Iwasawa theory, zeta elements for \(\mathbb G_m\), and the equivariant Tamagawa number conjecture ⋮ Refined abelian Stark conjectures and the equivariant leading term conjecture of Burns ⋮ A refined Beilinson–Bloch conjecture for motives of modular forms ⋮ A proof of the refined class number formula of Gross ⋮ Linear forms on Sinnott's module ⋮ The equivariant Tamagawa number conjecture and the extended abelian Stark conjecture ⋮ The equivariant Tamagawa number conjecture for abelian extensions of imaginary quadratic fields ⋮ On derivatives of Artin \(L\)-series ⋮ Contracted ideals of \(p\)-adic integral group rings ⋮ Congruences for critical values of higher derivatives of twisted Hasse–Weil $L$-functions, II ⋮ THE EQUIVALENCE OF RUBIN'S CONJECTURE AND THE ETNC/LRNC FOR CERTAIN BIQUADRATIC EXTENSIONS ⋮ Stickelberger elements for \(\mathbb Z^d_p\)-extensions of function fields ⋮ Congruences between derivatives of geometric \(L\)-functions. With an appendix by David Burns, King Fai Lai and Ki-Seng Tan ⋮ On the equivariant Tamagawa number conjecture in tame CM-extensions ⋮ Numerical evidence for higher order Stark-type conjectures ⋮ On higher order Stickelberger-type theorems ⋮ Generalized Stark formulae over function fields ⋮ THE FRACTIONAL GALOIS IDEAL FOR ARBITRARY ORDER OF VANISHING ⋮ Special values of Abelian \(L\)-functions at \(s=0\) ⋮ On the cyclotomic main conjecture for the prime 2 ⋮ Annihilators of the Ideal Class Group of a Cyclic Extension of an Imaginary Quadratic Field ⋮ Stickelberger elements over rational function fields

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 \(s=0\)
• Iwasawa theory of \(p\)-adic representations over a local field
• Determinant functors on exact categories and their extensions to categories of bounded complexes
• On the equivariant Tamagawa number conjecture for Tate motives
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• On the refined class number formula for global function fields
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• On the equivariant Tamagawa number conjecture for Abelian extensions of a quadratic imaginary field
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• The Rubin--Stark conjecture for a special class of function field extensions
• Explicit units and the equivariant Tamagawa number conjecture
• Base change for Stark-type conjectures "over \mathbb{Z}"
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