Distribution of zeroes of Rademacher Taylor series
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 25 (2016) no. 4, pp. 759-784.

Nous trouvons l’asymptotique de la fonction de comptage de zéros pour les fonctions entières aléatoires représentées par des séries de Taylor du type de Rademacher. Nous donnons aussi l’asymptotique pour la fonction de comptage à poids, qui prend en compte les arguments des zéros. Ces résultats répondent à certaines questions laissées ouvertes après le travail novateur de Littlewood et Offord en 1948.

Les preuves sont basées sur notre résultat récent sur l’intégrabilité logarithmique de séries de Fourier du type de Rademacher.

We find the asymptotics of the counting function of zeroes of random entire functions represented by Rademacher Taylor series. We also give the asymptotics of the weighted counting function, which takes into account the arguments of zeroes. These results answer several questions left open after the pioneering work of Littlewood and Offord of 1948.

The proofs are based on our recent result on the logarithmic integrability of Rademacher Fourier series.

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     author = {Nazarov, Fedor and Nishry, Alon and Sodin, Mikhail},
     title = {Distribution of zeroes of {Rademacher} {Taylor} series},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {759--784},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
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Nazarov, Fedor; Nishry, Alon; Sodin, Mikhail. Distribution of zeroes of Rademacher Taylor series. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 25 (2016) no. 4, pp. 759-784. doi : 10.5802/afst.1510. http://archive.numdam.org/articles/10.5802/afst.1510/

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