On a conjecture of Faulhuber and Steinerberger on the logarithmic derivative of <i>ϑ</i><sub>4</sub>

Anne-Maria Ernvall-Hytönen; Esa V. Vesalainen

doi:10.1016/j.crma.2018.04.006

Number theory/Mathematical analysis

On a conjecture of Faulhuber and Steinerberger on the logarithmic derivative of ϑ₄
[De la conjecture de Faulhuber et Steinerberger sur la dérivée logarithmique de ϑ₄]

Présenté par : the Editorial Board

Anne-Maria Ernvall-Hytönen ¹ ; Esa V. Vesalainen ¹

¹ Matematik och Statistik, Åbo Akademi University, Domkyrkotorget 1, 20500 Åbo, Finland

Comptes Rendus. Mathématique, Volume 356 (2018) no. 5, pp. 457-462.

Résumé
Abstract

Faulhuber et Steinerberger ont conjecturé que la dérivée logarithmique de $ϑ_{4}$ possède la propriété selon laquelle $y^{2} ϑ_{4}^{'} (y) / ϑ_{4} (y)$ est strictement décroissant et strictement convexe. Dans cette courte note, nous démontrons cette conjecture.

Faulhuber and Steinerberger conjectured that the logarithmic derivative of $ϑ_{4}$ has the property that $y^{2} ϑ_{4}^{'} (y) / ϑ_{4} (y)$ is strictly decreasing and strictly convex. In this small note, we prove this conjecture.

Reçu le : 2018-01-24
Accepté le : 2018-04-11
Publié le : 2018-04-16

DOI : 10.1016/j.crma.2018.04.006

Affiliations des auteurs :

Anne-Maria Ernvall-Hytönen ¹ ; Esa V. Vesalainen ¹

¹ Matematik och Statistik, Åbo Akademi University, Domkyrkotorget 1, 20500 Åbo, Finland

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     author = {Anne-Maria Ernvall-Hyt\"onen and Esa V. Vesalainen},
     title = {On a conjecture of {Faulhuber} and {Steinerberger} on the logarithmic derivative of \protect\emph{\ensuremath{\vartheta}}\protect\textsubscript{4}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {457--462},
     publisher = {Elsevier},
     volume = {356},
     number = {5},
     year = {2018},
     doi = {10.1016/j.crma.2018.04.006},
     language = {en},
}

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Anne-Maria Ernvall-Hytönen; Esa V. Vesalainen. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.04.006/

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Cité par Sources :

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

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