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On the Complex Conjugate Zeros of the Partial Theta Function

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Abstract

We prove that (1) for any q ∈ (0, 1), all complex conjugate pairs of zeros of the partial theta function \(\theta (q,x): = \sum\nolimits_{j = 0}^\infty {{q^{j(j + 1)/2}}{x^j}}\) belong to the set {Re x ∈ (−5792.7,0), |Im x| < 132} ∪ {|x| < 18} and (2) for any q ∈ (−1,0), they belong to the rectangle {|Re x| < 364.2, |Im x| < 132}.

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Authors and Affiliations

  1. Université Côte d’Azur, CNRS, LJAD, Nice, France

    V. P. Rostov

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  1. V. P. Rostov
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Correspondence to V. P. Rostov.

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Text Copyright © The Author(s), 2019. Published in Funktsional’nyi Analiz i Ego Prilozheniya, 2019, Vol. 53, No. 2, pp. 87–91.

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Rostov, V.P. On the Complex Conjugate Zeros of the Partial Theta Function. Funct Anal Its Appl 53, 149–152 (2019). https://doi.org/10.1134/S0016266319020102

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  • DOI: https://doi.org/10.1134/S0016266319020102

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