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On the Values of Certain Lambert Series

Volume 8, Number 2 (2009), 80 - 89

On the Values of Certain Lambert Series

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Abstract

Using relations between Lambert series, Eisenstein series, and the WeierstrassÃ- function, we evaluate the sums of certain infinite series in terms of Bernoulli numbers, Hurwitz numbers, and the arc length of the lemniscate.