EXCEPTIONAL ZEROS OF L-SERIES AND BERNOULLI-CARLITZ NUMBERS

Abstract : Bernoulli-Carlitz numbers were introduced by L. Carlitz in 1935, they are the 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. We then show that the " exceptional zeros " of certain L-series are intimately connected to the Bernoulli-Carlitz numbers.
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  • ARXIV : 1511.06209

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Bruno Anglès, Tuan Ngo Dac, Floric Tavares Ribeiro. EXCEPTIONAL ZEROS OF L-SERIES AND BERNOULLI-CARLITZ NUMBERS. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, Scuola Normale Superiore 2019, 19 (3), pp.981-1024. ⟨hal-01404891⟩

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