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Congruences for the coefficients of the Gordon and McIntosh mock theta function $\xi(q)$
, 2020Recently Gordon and McIntosh introduced the third order mock theta function $\xi(q)$ defined by $$ \xi(q)=1+2\sum_{n=1}^{\infty}\frac{q^{6n^2-6n+1}}{(q;q^6)_{n}(q^5;q^6)_{n}}.
R. Silva, James A. Sellers
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On multiple zeros of a partial theta function
, 2016We consider the partial theta function θ(q, x) := ∑j=0∞qj(j+1)/2xj, where x ∈ ℂ is a variable and q ∈ ℂ, 0 < |q| < 1, is a parameter. We show that, for any fixed q, if ζ is a multiple zero of the function θ(q, · ), then |ζ| ≤ 811.
V. Kostov
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Identities involving mock theta functions and theta functions
Proceedings of the American Mathematical Society, 2023In this paper, we first present new representations for several mock theta functions. In view of the sign flips on these identities, some interesting results involving theta functions are established by new Bailey pairs and Watson’s 8 ϕ 7 _8\phi _7 transformation ...
Song, Hanfei, Wang, Chun
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On the spectrum of a partial theta function
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2014The bivariate series defines a partial theta function. For fixed q, θ(q, ·) is an entire function. We show that for ∣q∣ ≤ 0.108 the function θ(q, ·) has no multiple zeros.
V. Kostov
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Operator $$\theta $$-Hölder functions
Banach Journal of Mathematical Analysis, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Huang, J., Sukochev, F.
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Fine’s function and partial theta function
Proceedings of the American Mathematical Society, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chan, Heng Huat +3 more
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