On Multiple Zeros of a Partial Theta Function
Funkcionalʹnyj analiz i ego priloženiâ, Tome 50 (2016) no. 2, pp. 84-88
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We consider the partial theta function $\theta (q,x):=\sum_{j=0}^{\infty}q^{j(j+1)/2}x^j$, where $x\in \mathbb{C}$ is a variable and $q\in \mathbb{C}$, $0|q|1$, is a parameter. We show that, for any fixed $q$, if $\zeta$ is a multiple zero of the function $\theta (q,\cdot)$, then $|\zeta |\le 8^{11}$.
Keywords:
partial theta function, multiple zero, series.
@article{FAA_2016_50_2_a7,
author = {V. P. Kostov},
title = {On {Multiple} {Zeros} of a {Partial} {Theta} {Function}},
journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
pages = {84--88},
publisher = {mathdoc},
volume = {50},
number = {2},
year = {2016},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FAA_2016_50_2_a7/}
}
V. P. Kostov. On Multiple Zeros of a Partial Theta Function. Funkcionalʹnyj analiz i ego priloženiâ, Tome 50 (2016) no. 2, pp. 84-88. http://geodesic.mathdoc.fr/item/FAA_2016_50_2_a7/