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Arithmetic of positive characteristic
$L$-series values in Tate algebras
- Part of
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- Journal:
- Compositio Mathematica / Volume 152 / Issue 1 / January 2016
- Published online by Cambridge University Press:
- 07 September 2015, pp. 1-61
- Print publication:
- January 2016
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- Article
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The second author has recently introduced a new class of
$L$-series in the arithmetic theory of function fields over finite fields. We show that the values at one of these 
$L$-series encode arithmetic information of a generalization of Drinfeld modules defined over Tate algebras that we introduce (the coefficients can be chosen in a Tate algebra). This enables us to generalize Anderson’s log-algebraicity theorem and an analogue of the Herbrand–Ribet theorem recently obtained by Taelman.
