## 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.

### MSC:

 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

### Keywords:

abelian $$t$$-modules; shtukas; special values
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### References:

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