Asymptotic representations for Fibonacci reciprocal sums and Euler’s formulas for zeta values
Journal de théorie des nombres de Bordeaux, Volume 21 (2009) no. 1, p. 145-157

We present asymptotic representations for certain reciprocal sums of Fibonacci numbers and of Lucas numbers as a parameter tends to a critical value. As limiting cases of our results, we obtain Euler’s formulas for values of zeta functions.

Nous présentons les représentations asymptotiques pour certaines sommes des réciproques des nombres de Fibonacci et des nombres de Lucas quand un paramètre tend vers une valeur critique. Comme cas limite de nos résultats, nous obtenons les formules d’Euler pour les valeurs des fonctions de zeta.

@article{JTNB_2009__21_1_145_0,
     author = {Elsner, Carsten and Shimomura, Shun and Shiokawa, Iekata},
     title = {Asymptotic representations for Fibonacci reciprocal sums and Euler's formulas for zeta values},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     publisher = {Universit\'e Bordeaux 1},
     volume = {21},
     number = {1},
     year = {2009},
     pages = {145-157},
     doi = {10.5802/jtnb.663},
     zbl = {1233.11018},
     mrnumber = {2537709},
     zbl = {pre05620674},
     language = {en},
     url = {http://www.numdam.org/item/JTNB_2009__21_1_145_0}
}
Elsner, Carsten; Shimomura, Shun; Shiokawa, Iekata. Asymptotic representations for Fibonacci reciprocal sums and Euler’s formulas for zeta values. Journal de théorie des nombres de Bordeaux, Volume 21 (2009) no. 1, pp. 145-157. doi : 10.5802/jtnb.663. http://www.numdam.org/item/JTNB_2009__21_1_145_0/

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