A q-analog of Euler's decomposition formula for the double zeta function

Details A q-analog of Euler's decomposition formula for the double zeta function A q-analog of Euler's decomposition formula for the double zeta function

2005-01-31

arxiv.org/abs/math/0502002v1

International Journal of Mathematics and Mathematical Sciences, 2005:21 (2005), pp. 3453--3458. MR2206867 (2006k:11174)

Mathematics

Number Theory

6 pages

Scientific paper

10.1155/IJMMS.2005.3453

The double zeta function was first studied by Euler in response to a letter from Goldbach in 1742. One of Euler's results for this function is a decomposition formula, which expresses the product of two values of the Riemann zeta function as a finite sum of double zeta values involving binomial coefficients. In this note, we establish a q-analog of Euler's decomposition formula. More specifically, we show that Euler's decomposition formula can be extended to what might be referred to as a ``double q-zeta function'' in such a way that Euler's formula is recovered in the limit as q tends to 1.

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