Functional identities for L-series values in positive characteristic

Bruno Angles (1) , Federico Pellarin (2)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 CTN - Combinatoire, théorie des nombres

In this paper we show the existence of functional relations for a class of L-series introduced by the second author. Our results will be applied to obtain a new class of congruences for Bernoulli-Carlitz fractions, and an analytic conjecture is stated, implying an interesting behavior of such fractions modulo prime ideals of Fq[T].

Mots clés: Anderson-Thakur function; L-functions in positive characteristic; Function fields of positive characteristic

Domaines: Théorie des nombres [math.NT]

Bruno Angles, Federico Pellarin. Functional identities for L-series values in positive characteristic. Journal of Number Theory, 2014, 142, pp.223-251. ⟨10.1016/j.jnt.2014.03.004⟩. ⟨hal-00955673⟩