Multiple zeta-functions associated with linear recurrence sequences and the vectorial sum formula.

Driss Essouabri (1) , Kohji Matsumoto (2) , Hirofumi Tsumura (3)

1 CTN - Combinatoire, théorie des nombres
2 Graduate School of Mathematics, Nagoya University,
3 Department of Mathematics and Information Sciences, Tokyo Metropolitan University

We prove the holomorphic continuation of certain multi-variable multiple zeta-functions whose coefficients satisfy a suitable recurrence condition. Actually we introduce more general vectorial zeta-functions, and prove their holomorphic continuation. Moreover we show a vectorial sum formula among those vectorial zeta-functions, from which some generalizations of the classical sum formula can be deduced.

Mots clés: sum formulas.; Fibonacci numbers; recurrence sequences; sum formulas; holomorphic continuation; Zeta-functions

Domaines: Théorie des nombres [math.NT]

Driss Essouabri, Kohji Matsumoto, Hirofumi Tsumura. Multiple zeta-functions associated with linear recurrence sequences and the vectorial sum formula.. Canadian Journal of Mathematics, 2011, 63 (2), p. 241-276. ⟨hal-00947516⟩