$L$-级数的例外零点与 Bernoulli-Carlitz 数
数论
2015-12-11 v2
摘要
Bernoulli-Carlitz 数由 L. Carlitz 于 1935 年引入，它们是 Bernoulli 数在正特征下的类比。我们证明了 F. Pellarin 和第一作者提出的关于 Bernoulli-Carlitz 数族在给定素数模下非零的猜想。随后我们证明了某些 -级数的“例外零点”与 Bernoulli-Carlitz 数密切相关。
引用
@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}
}
备注
with an appendix by B. Angl\`es, D. Goss, F. Pellarin and F. Tavares Ribeiro : "The digit principle and derivatives of certain $L$-series"