On the log-concavity of a Jacobi theta function

DOI10.1090/S0025-5718-2013-02681-6zbMath1278.30028OpenAlexW2050192334MaRDI QIDQ5326509

Mark W. Coffey, George Csordas

Publication date: 6 August 2013

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-2013-02681-6

zbMATH Keywords

log-concavityreal zerosJacobi theta functionRiemann \(\Xi\)-functionTurán inequalityadmissible kernel

Mathematics Subject Classification ID

Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Real polynomials: location of zeros (26C10) Elliptic functions and integrals (33E05) Representations of entire functions of one complex variable by series and integrals (30D10) Special classes of entire functions of one complex variable and growth estimates (30D15)

Related Items (4)

Optimal Gabor frame bounds for separable lattices and estimates for Jacobi theta functions ⋮ Fourier transforms of positive definite kernels and the Riemann \(\xi\)-function ⋮ Extremal determinants of Laplace-Beltrami operators for rectangular tori ⋮ On a conjecture of Faulhuber and Steinerberger on the logarithmic derivative of \(\vartheta_{4}\)

Cites Work

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• The Riemann Hypothesis and the Turan Inequalities
• Properties of Probability Distributions with Monotone Hazard Rate
• On the Asymptotic Behavior of the Riemann ξ-Function
• Inequalities: theory of majorization and its applications

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