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Zeros of the lerch transcendent function

Abstract

We investigate the distribution of zeros of the Lerch transcendent function We find an upper and lower estimates of zeros of the function Φ(q,s,a) in any rectangle {s : σ1 < Re s < σ2 ≤ 1.73…, 0 < Im s ≤ T}. Further we are interested in a computer calculations concerning the zeros of Φ(q,s,α) in {s: Re s > 1, 0 < Im s ≤ 1000}.

Keyword : Polylogarithm, Lerch transcendent, zero distribution

How to Cite
Garunkštis, R., & Grigutis, A. (2012). Zeros of the lerch transcendent function. Mathematical Modelling and Analysis, 17(2), 245-250. https://doi.org/10.3846/13926292.2012.662532
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Apr 1, 2012
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