On a conjecture of Faulhuber and Steinerberger on the logarithmic derivative of ϑ4

Anne-Maria Ernvall-Hytönen,Esa V. Vesalainen

Comptes Rendus Mathematique（2018）

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摘要

Faulhuber and Steinerberger conjectured that the logarithmic derivative of ϑ4 has the property that y2ϑ4′(y)/ϑ4(y) is strictly decreasing and strictly convex. In this small note, we prove this conjecture.

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