scientific article

zbMath0569.12008MaRDI QIDQ3686794

David R. Hayes

Publication date: 1985

Full work available at URL: http://www.numdam.org/item?id=CM_1985__55_2_209_0

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zbMATH Keywords

unitsIwasawa theorycyclotomic function fieldsDrinfeld modulesideal class groupsStickelberger elementp-adic group ringelliptic modulespartial zeta-functionsStark's Abelian conjectures

Mathematics Subject Classification ID

Cyclotomic function fields (class groups, Bernoulli objects, etc.) (11R60) Drinfel'd modules; higher-dimensional motives, etc. (11G09) Zeta functions and (L)-functions of number fields (11R42) Iwasawa theory (11R23)

Related Items (35)

Cyclotomic units and Stickelberger ideals of global function fields ⋮ On the index of cyclotomic units in characteristic \(p\) and its applications ⋮ Punctured distributions of global function fields ⋮ Fourier series and the special values of \(L\)-functions ⋮ Periods of \(t\)-motives and transcendence ⋮ The refined \(\mathfrak p\)-adic abelian Stark conjecture in function fields ⋮ Class number growth of a family of \(\mathbb{Z}_p\)-extensions over global function fields ⋮ David R. Hayes: some remarks on his life and work ⋮ On Kronecker terms over global function fields ⋮ A rapid introduction to Drinfeld modules, \(t\)-modules, and \(t\)-motives ⋮ Aspects of Iwasawa theory over function fields ⋮ Index-modules and applications ⋮ Distributions on a global field ⋮ Stickelberger ideals and relative class numbers in function fields ⋮ Arithmetic of Gamma, Zeta and Multizeta Values for Function Fields ⋮ Norm and trace of the \(j\)-invariants of Drinfeld modules associated to hyperelliptic curves ⋮ Integrality of Stickelberger elements attached to unramified extensions of imaginary quadratic fields ⋮ The Rubin--Stark conjecture for a special class of function field extensions ⋮ Double complex and gamma-monomials in global function fields ⋮ The theta divisor and the Stickelberger theorem ⋮ Sign functions of imaginary quadratic fields and applications. ⋮ Euler systems in global function fields ⋮ Cyclotomic units in function fields ⋮ Shtukas and Jacobi sums ⋮ Gauss sums for function fields ⋮ Zsigmondy theorem for arithmetic dynamics induced by a drinfeld module ⋮ An extension of the first-order Stark conjecture ⋮ L-functions of p-adic characters and geometric Iwasawa theory ⋮ Polynomials defining many units in function fields ⋮ Remarks on rank one Drinfeld modules and their torsion elements ⋮ An alternate approach to solitons for \(\mathbb F_q [t\)] ⋮ On the Frobenius Endomorphisms of Fermat and Artin-Schreier Curves ⋮ Class-groups of function fields ⋮ On the holomorphy on certain non-Abelian L-series ⋮ Annihilators of the ideal class group of a cyclic extension of a global function field

Cites Work

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• The Stark conjectures on Artin \(L\)-functions at \(s=0\). Lecture notes of a course in Orsay edited by Dominique Bernardi and Norbert Schappacher.
• On a new type of \(L\)-function for algebraic curves over finite fields
• The \(\Gamma\)-ideal and special zeta-values
• Distributions on rational function fields
• The class number of cyclotomic function fields
• \(L\)-functions at \(s=1\). IV: First derivatives at \(s=0\)
• Units and class groups in cyclotomic function fields
• Analytic class number formulas in function fields
• Explicit Class Field Theory for Rational Function Fields
• ELLIPTIC MODULES

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