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

Carsten Elsner, Shun Shimomura, Iekata Shiokawa

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)145-157
Number of pages13
JournalJournal de Theorie des Nombres de Bordeaux
Volume21
Issue number1
DOIs
Publication statusPublished - 2009

Fingerprint

Lucas numbers
Asymptotic Representation
Lame number
Riemann zeta function
Critical value
Limiting
Tend

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Asymptotic representations for fibonacci reciprocal sums and euler’s formulas for zeta values. / Elsner, Carsten; Shimomura, Shun; Shiokawa, Iekata.

In: Journal de Theorie des Nombres de Bordeaux, Vol. 21, No. 1, 2009, p. 145-157.

Research output: Contribution to journalArticle

Elsner, Carsten ; Shimomura, Shun ; Shiokawa, Iekata. / Asymptotic representations for fibonacci reciprocal sums and euler’s formulas for zeta values. In: Journal de Theorie des Nombres de Bordeaux. 2009 ; Vol. 21, No. 1. pp. 145-157.
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