Special \(L\)-values of abelian \(t\)-modules. (English) Zbl 1360.11074

Summary: We prove a formula for the \(\infty\)-adic special \(L\)-value of abelian \(t\)-modules. This gives function field analogues of the class number formula. We also express it in terms of the extension groups of shtukas.


11G09 Drinfel’d modules; higher-dimensional motives, etc.
11R58 Arithmetic theory of algebraic function fields
13C99 Theory of modules and ideals in commutative rings
14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)
14F40 de Rham cohomology and algebraic geometry
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