On the number of prime factors of summands of partitions
Cécile Dartyge[1]; András Sárközy[2]; Mihály Szalay[2]
- [1] Institut Élie Cartan Université Henri Poincaré–Nancy 1 BP 239 54506 Vandœuvre Cedex, France
- [2] Department of Algebra and Number Theory Eötvös Loránd University H-1117 Budapest Pázmány Péter sétány 1/C, Hungary
Journal de Théorie des Nombres de Bordeaux (2006)
- Volume: 18, Issue: 1, page 73-87
- ISSN: 1246-7405
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topDartyge, Cécile, Sárközy, András, and Szalay, Mihály. "On the number of prime factors of summands of partitions." Journal de Théorie des Nombres de Bordeaux 18.1 (2006): 73-87. <http://eudml.org/doc/249636>.
@article{Dartyge2006,
abstract = {We present various results on the number of prime factors of the parts of a partition of an integer. We study the parity of this number, the extremal orders and we prove a Hardy-Ramanujan type theorem. These results show that for almost all partitions of an integer the sequence of the parts satisfies similar arithmetic properties as the sequence of natural numbers.},
affiliation = {Institut Élie Cartan Université Henri Poincaré–Nancy 1 BP 239 54506 Vandœuvre Cedex, France; Department of Algebra and Number Theory Eötvös Loránd University H-1117 Budapest Pázmány Péter sétány 1/C, Hungary; Department of Algebra and Number Theory Eötvös Loránd University H-1117 Budapest Pázmány Péter sétány 1/C, Hungary},
author = {Dartyge, Cécile, Sárközy, András, Szalay, Mihály},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {partitions; prime factors; Liouville function},
language = {eng},
number = {1},
pages = {73-87},
publisher = {Université Bordeaux 1},
title = {On the number of prime factors of summands of partitions},
url = {http://eudml.org/doc/249636},
volume = {18},
year = {2006},
}
TY - JOUR
AU - Dartyge, Cécile
AU - Sárközy, András
AU - Szalay, Mihály
TI - On the number of prime factors of summands of partitions
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2006
PB - Université Bordeaux 1
VL - 18
IS - 1
SP - 73
EP - 87
AB - We present various results on the number of prime factors of the parts of a partition of an integer. We study the parity of this number, the extremal orders and we prove a Hardy-Ramanujan type theorem. These results show that for almost all partitions of an integer the sequence of the parts satisfies similar arithmetic properties as the sequence of natural numbers.
LA - eng
KW - partitions; prime factors; Liouville function
UR - http://eudml.org/doc/249636
ER -
References
top- C. Dartyge, A. Sárközy, M. Szalay, On the distribution of the summands of partitions in residue classes. Acta Math. Hungar. 109 (2005), 215–237. Zbl1119.11061MR2187286
- P. Erdős, J. Lehner, The distribution of the number of summands in the partitions of a positive integer. Duke Math. Journal 8 (1941), 335–345. Zbl0025.10703MR4841
- M. Szalay, P. Turán, On some problems of the statistical theory of partitions with application to characters of the symmetric group II. Acta Math. Acad. Sci. Hungar. 29 (1977), 381–392. Zbl0371.10034MR506109
- M. Szalay, P. Turán, On some problems of the statistical theory of partitions with application to characters of the symmetric group III. Acta Math. Acad. Sci. Hungar. 32 (1978), 129–155. Zbl0391.10031MR505078
- G. Tenenbaum, Introduction à la théorie analytique et probabiliste des nombres, 2e édition. Cours spécialisés no 1, Société mathématique de France (1995). Zbl0880.11001MR1366197
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