Abstract
Bernoulli-Carlitz numbers were introduced by L. Carlitz in 1935. They are analogues in positive characteristic of Bernoulli numbers. We prove a conjecture formulated by F. Pellarin and the first author on the non-vanishing modulo a given prime of families of Bernoulli-Carlitz numbers. The proof is intimately connected to the arithmetic properties of the L-series introduced by F. Pellarin. Finally, we formulate a conjecture concerning the exceptional zeros of these L-series and prove it in various cases.
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