Arithmetic of positive characteristic $L$-series values in Tate algebras

By Bruno Anglès, F. Pellarin, Floric Tavares-Ribeiro. Compositio Mathematica, 2014

61 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/060adcaf3b5cc85d738f208536d13c8ce34a1af9

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In Computational Theory and Mathematics

1. Bruno Anglès
2. F. Pellarin

In Geometry and Topology

1. Bruno Anglès
2. F. Pellarin

Citations in the corpus

• Universal Gauss-Thakur sums and $$L$$L-series (2013, background): “For the background on Gauss-Thakur sums we refer to [9, Section 9.8].”