IPM - Institute for Research in Fundamental Sciences

“School of Mathematics”

Paper IPM / M / 8008

School of Mathematics

Title:

Irrationality of certain numbers that contain values of the di- and trilogarithm

Author(s):

1.	Kh. Hessami Pilehrood
2.	T. Hessami Pilehrood (Joint with W. Zudilin)

Status:

Published

Journal:

Math. Z.

Vol.:

254

Year:

2006

Pages:

299-313

Supported by:

IPM

Abstract:

We prove that, for z ∈ {1/2,2/3,3/4,4/5}, at least one of the two numbers

∞
∑
l=1

z^l

l²

+log(1−z)logz and

∞
∑
l=1

z^l

l³

log(1−z)log²z

is irrational.

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