Comptes Rendus
no. 5
Number theory
Parity of Schur's partition function
[Parité de la fonction de partition de Schur]

Présenté par : the Editorial Board

Shi-Chao Chen1
1 Institute of Contemporary Mathematics, School of Mathematics and Statistics, Henan University, Kaifeng, 475004, PR China
Comptes Rendus. Mathématique, Volume 357 (2019) no. 5, pp. 418-423.

Soit A(n) le nombre de partitions de Schur de n, c'est-à-dire le nombre de partitions de n en parts distinctes congrues à 1,2(mod3). Nous montrons que :

x(log⁡x)4748≪♯{0≤n≤x:A(2n+1) impair}≪x(log⁡x)12.

Let A(n) be the number of Schur's partitions of n, i.e. the number of partitions of n into distinct parts congruent to 1, 2(mod3). We prove

x(log⁡x)4748≪♯{0≤n≤x:A(2n+1) is odd}≪x(log⁡x)12.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2019.05.006
Shi-Chao Chen 1

1 Institute of Contemporary Mathematics, School of Mathematics and Statistics, Henan University, Kaifeng, 475004, PR China 
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Shi-Chao Chen. Parity of Schur's partition function. Comptes Rendus. Mathématique, Volume 357 (2019) no. 5, pp. 418-423. doi : 10.1016/j.crma.2019.05.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2019.05.006/

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