 |
 |
|
|
| HAL: hal-00558991, version 2 |
| arXiv: 1101.4557 |
| DOI: 10.5486/PMD.2011.5106 |
| Detailed view |  Export this paper |
 |
| Publ. Math. Debrecen 79, 3-4 (2011) 687-697 |
|
|
| Available versions: | v1 (2011-01-24) | v2 (2012-05-05) |
|
|
|
|
| On the counting function of sets with even partition functions |
|
|
| Fethi Ben Said 1Jean-Louis Nicolas 2 |
|
|
| (2011-10-10) |
|
|
|
| Let q be an odd positive integer and P \in F2[z] be of order q and such that P(0) = 1. We denote by A = A(P) the unique set of positive integers satisfying \sum_{n=0}^\infty p(A, n) z^n \equiv P(z) (mod 2), where p(A,n) is the number of partitions of n with parts in A. In [5], it is proved that if A(P, x) is the counting function of the set A(P) then A(P, x) << x(log x)^{-r/\phi(q)}, where r is the order of 2 modulo q and \phi is Euler's function. In this paper, we improve on the constant c=c(q) for which A(P,x) << x(log x)^{-c}. |
|
|
|
|
|
|
|
|
|
|
|
| 1: | Université de Monastir |
|
|
|
Faculté des Sciences de Monastir |
|
|
| 2: | Institut Camille Jordan (ICJ) |
|
|
|
CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées (INSA) - Lyon |
|
|
|
|
|
|
|
|
|
| Subject | : | Mathematics/Number Theory |
|
|
| sets with even partition functions – bad and semi-bad primes – order of a polynomial – Selberg-Delange formula. |
|
|
|
| Attached file list to this document: | ||||||||||
|
||||||||||
|
|
|
| hal-00558991, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00558991 | |
| oai:hal.archives-ouvertes.fr:hal-00558991 | |
| From: Jean-Louis Nicolas | |
| Submitted on: Friday, 4 May 2012 17:15:53 | |
| Updated on: Saturday, 5 May 2012 07:44:28 | |
