Number of two-dimensional irreducible representations of the fundamental group of a curve over a finite field

DOI10.1007/BF01106161zbMath0479.14017MaRDI QIDQ1161572

Vladimir Drinfeld

Publication date: 1982

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

zbMATH Keywords

finite fieldSelberg trace formulafundamental group of a curvel-adic representations

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Finite ground fields in algebraic geometry (14G15) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Coverings of curves, fundamental group (14H30) Zeta functions and (L)-functions of number fields (11R42) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Langlands-Weil conjectures, nonabelian class field theory (11R39) Linear algebraic groups over adèles and other rings and schemes (20G35)

Related Items (9)

Explicit forms of the trace formula for \(\mathrm{GL}(2)\) ⋮ Number of irreducible \(\ell\)-adic local systems on a curve ⋮ Counting local systems with principal unipotent local monodromy ⋮ Counting local systems via the trace formula ⋮ Local systems with tame, and a unipotent, local monodromy ⋮ Counting local systems with tame ramification ⋮ On the Ramanujan conjecture for automorphic forms over function fields I. Geometry ⋮ Notes on Motives in Finite Characteristic ⋮ Higher-rank zeta functions and SL _n -zeta functions for curves

Cites Work

• Expansion in the characteristic functions of the momentless problem in the case of axially symmetric oscillations of a thin shell
• Automorphic forms on GL (2)
• Les Constantes des Equations Fonctionnelles des Fonctions L

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