On a conjecture of Faulhuber and Steinerberger on the logarithmic derivative of $\vartheta_4$

Anne-Maria Ernvall-Hyt\"onen; Esa V. Vesalainen

arxiv: 1709.05194 · v2 · pith:3BKHA733new · submitted 2017-09-15 · 🧮 math.NT

On a conjecture of Faulhuber and Steinerberger on the logarithmic derivative of vartheta₄

Anne-Maria Ernvall-Hyt\"onen , Esa V. Vesalainen This is my paper

classification 🧮 math.NT

keywords varthetaconjecturederivativefaulhuberlogarithmicsteinerbergerstrictlyconjectured

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Faulhuber and Steinerberger conjectured that the logarithmic derivative of $\vartheta_4$ has the property that $y^2\,\vartheta_4'(y)/\vartheta_4(y)$ is strictly decreasing and strictly convex. In this small note, we prove this conjecture.

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On a conjecture of Faulhuber and Steinerberger on the logarithmic derivative of vartheta₄

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