Short notes

Linear independence of values of Lerch functions

E. A. Ulanskii

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The number of linearly independent numbers among $1,\Phi _1\left( z,\frac{p}{q}\right),\ldots,\Phi _a\left( z,\frac{p}{q}\right)$ is estimated depending on a natural number $a$, where $\Phi _s \left(z,\frac{p}{q}\right),\ s=1,2,\ldots$, are Lerch functions.

Key words: Lerch functions, generalized polylogarithms, linear independence.

UDC: 517.521

Received: 02.04.2007
Revised: 27.06.2007

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