English

Combinatorial proof of the transcendence of $L(1,\chi_s)/\Pi$

Combinatorics 2016-06-21 v2 Number Theory

Abstract

We give a combinatorial proof of the transcendence of L(1,χs)/ΠL(1,\chi_s)/\Pi, where L(1,χs)L(1,\chi_s) (resp. Π\Pi) is the analogue in characteristic pp of the function LL of Dirichlet (resp. π\pi). This result has been proven by G. Damamme using the criteria of de Mathan. Our proof is based on the Theorem of Christol and another property of kk-automatic sequences.

Keywords

Cite

@article{arxiv.1606.04137,
  title  = {Combinatorial proof of the transcendence of $L(1,\chi_s)/\Pi$},
  author = {Yining Hu},
  journal= {arXiv preprint arXiv:1606.04137},
  year   = {2016}
}