Journal of Integer Sequences, Vol. 22 (2019), Article 19.3.6

The Riemann Zeta Function and the Fractional Part of Rational Powers

Tal Barnea
United Kingdom


We use elementary methods to find an explicit formula for the second term of the continued fraction of the Riemann zeta function over positive integers, with only finitely many exceptions. As a corollary to this, we find connections between the Riemann zeta function and the fractional parts of rational powers.

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(Concerned with sequence A013697.)

Received November 10 2018; revised version received March 9 2019. Published in Journal of Integer Sequences, May 20 2019.

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