The refined \(\mathfrak p\)-adic abelian Stark conjecture in function fields

DOI10.1007/BF01394274zbMath0666.12009WikidataQ123200968 ScholiaQ123200968MaRDI QIDQ1116975

David R. Hayes

Publication date: 1988

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

Full work available at URL: https://eudml.org/doc/143635

zbMATH Keywords

function fieldsDrinfeld modules\(\mathfrak p\)-adic abelian Stark conjecture

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Units and factorization (11R27) Drinfel'd modules; higher-dimensional motives, etc. (11G09) Zeta functions and (L)-functions of number fields (11R42) Cyclotomic extensions (11R18)

Related Items

\(p\)-adic Abelian Stark conjectures at \(s=1\) ⋮ Refined class number formulas for \(\mathbb{G}_m\) ⋮ ANOTHER LOOK AT GROSS–STARK UNITS OVER THE NUMBER FIELD ℚ ⋮ Congruences between derivatives of abelian \(L\)-functions at \(s =0\) ⋮ David R. Hayes: some remarks on his life and work ⋮ A conjectural product formula for Brumer-Stark units over real quadratic fields ⋮ Gross' conjecture for extensions ramified over four points of \(\mathbb P^1\) ⋮ 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 Tate's refinement for a conjecture of Gross and its generalization ⋮ The rigid analytical regulator and \(K_2\) of Drinfeld modular curves ⋮ Proof of an exceptional zero conjecture for elliptic curves over function fields ⋮ Generalized Stark formulae over function fields ⋮ Stickelberger elements over rational function fields ⋮ Rank one elliptic \(A\)-modules and \(A\)-harmonic series

Cites Work

• The arithmetic of function fields. II: The 'cyclotomic' theory
• Values of abelian \(L\)-functions at negative integers over totally real fields
• Units and class groups in cyclotomic function fields
• Gauss sums and the p-adic \(\Gamma\)-function
• Values at negative integers of zeta functions and \(p\)-adic zeta functions
• Explicit Class Field Theory for Rational Function Fields
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