Asymptotic representations for fibonacci reciprocal sums and euler’s formulas for zeta values

Carsten Elsner; Shun Shimomura; Iekata Shiokawa

doi:10.5802/jtnb.663

Asymptotic representations for fibonacci reciprocal sums and euler’s formulas for zeta values

Carsten Elsner, Shun Shimomura, Iekata Shiokawa

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	145-157
Number of pages	13
Journal	Journal de Theorie des Nombres de Bordeaux
Volume	21
Issue number	1
DOIs	https://doi.org/10.5802/jtnb.663
Publication status	Published - 2009
Externally published	Yes

ASJC Scopus subject areas

Algebra and Number Theory

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10.5802/jtnb.663

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title = "Asymptotic representations for fibonacci reciprocal sums and euler{\textquoteright}s formulas for zeta values",

abstract = "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{\textquoteright}s formulas for values of zeta functions.",

author = "Carsten Elsner and Shun Shimomura and Iekata Shiokawa",

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AU - Elsner, Carsten

AU - Shimomura, Shun

AU - Shiokawa, Iekata

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Asymptotic representations for fibonacci reciprocal sums and euler’s formulas for zeta values

Abstract

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