Number theory/Mathematical analysis
On a conjecture of Faulhuber and Steinerberger on the logarithmic derivative of ϑ4
Comptes Rendus. Mathématique, Volume 356 (2018) no. 5, pp. 457-462.

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.

Faulhuber et Steinerberger ont conjecturé que la dérivée logarithmique de ϑ4 possède la propriété selon laquelle y2ϑ4(y)/ϑ4(y) est strictement décroissant et strictement convexe. Dans cette courte note, nous démontrons cette conjecture.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2018.04.006
Ernvall-Hytönen, Anne-Maria 1; Vesalainen, Esa V. 1

1 Matematik och Statistik, Åbo Akademi University, Domkyrkotorget 1, 20500 Åbo, Finland
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Ernvall-Hytönen, Anne-Maria; Vesalainen, Esa V. On a conjecture of Faulhuber and Steinerberger on the logarithmic derivative of ϑ4. Comptes Rendus. Mathématique, Volume 356 (2018) no. 5, pp. 457-462. doi : 10.1016/j.crma.2018.04.006. http://www.numdam.org/articles/10.1016/j.crma.2018.04.006/

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This work was supported by the Academy of Finland project 303820, and E. V. V. was supported by the Magnus Ehrnrooth Foundation.