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}.
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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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}.