Functional identities for \(L\)-series values in positive characteristic. (English) Zbl 1385.11057

Anglès, Bruno; Pellarin, Federico

J. Number Theory 142, 223-251 (2014).

Summary: In this paper we show the existence of functional relations for a class of \(L\)-series introduced by the second author in [Ann. Math. (2) 176, No. 3, 2055–2093 (2012; Zbl 1336.11064)]. 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 \(\mathbb{F}_q [\theta]\).

MSC:

11M38	Zeta and \(L\)-functions in characteristic \(p\)
11F52	Modular forms associated to Drinfel’d modules
14L05	Formal groups, \(p\)-divisible groups

Keywords:

Anderson-Thakur function; \(L\)-functions in positive characteristic; function fields of positive characteristic

Citations:

Zbl 1336.11064

References:

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