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Irrationality of certain numbers that contain values of the di- and trilogarithm. (English summary) Math. Z. 254 (2006), no. 2, 299–313. The authors prove that, for z ∈ {1/2, 2/3, 3/4, 4/5}, at least one of the two numbers Li2(z) + log(1 − z) log(z), Li3(z) + 1 2 log(1 − z) log(z)2, is irrational, where Lis(z) = ∑∞ k=1 zk /ks. In the case z = 1/2, this improves the previous result of S. Fischler and the reviewer [J. Math. Pures Appl. (9) 82 (2003), no. 10, 1369–1394; MR2020926 (2004m:11114)] that at least one of the three number

Year: 2013

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