Geodesic
Multiple Zeta-Functions Associated with Linear Recurrence Sequences and the Vectorial Sum Formula
Canadian journal of mathematics, Tome 63 (2011) no. 2, pp. 241-276

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DOI

We prove the holomorphic continuation of certain multi-variable multiple zeta-functions whose coefficients satisfy a suitable recurrence condition. In fact, 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.
DOI : 10.4153/CJM-2010-085-1
Mots-clés : 11M41, 40B05, 11B39, Zeta-functions, holomorphic continuation, recurrence sequences, Fibonacci numbers, sum formulas 
Essouabri, Driss; Matsumoto, Kohji; Tsumura, Hirofumi. Multiple Zeta-Functions Associated with Linear Recurrence Sequences and the Vectorial Sum Formula. Canadian journal of mathematics, Tome 63 (2011) no. 2, pp. 241-276. doi: 10.4153/CJM-2010-085-1
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     title = {Multiple {Zeta-Functions} {Associated} with {Linear} {Recurrence} {Sequences} and the {Vectorial} {Sum} {Formula}},
     journal = {Canadian journal of mathematics},
     pages = {241--276},
     year = {2011},
     volume = {63},
     number = {2},
     doi = {10.4153/CJM-2010-085-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2010-085-1/}
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