Exceptional Zeros of $L$-series and Bernoulli-Carlitz Numbers
Number Theory
2015-12-11 v2
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 -series are intimately connected to the Bernoulli-Carlitz numbers.
Cite
@article{arxiv.1511.06209,
title = {Exceptional Zeros of $L$-series and Bernoulli-Carlitz Numbers},
author = {Bruno Anglès and Tuan Ngo Dac and Floric Tavares Ribeiro},
journal= {arXiv preprint arXiv:1511.06209},
year = {2015}
}
Comments
with an appendix by B. Angl\`es, D. Goss, F. Pellarin and F. Tavares Ribeiro : "The digit principle and derivatives of certain $L$-series"