Integer partitions detect the primes

We show that integer partitions, the fundamental building blocks in additive number theory, detect prime numbers in an unexpected way. Answering a question of Schneider, we show that the primes are the solutions to special equations in partition functions. For example, an integer ≥ 2 is prime if and...

Celý popis

Uložené v:
Podrobná bibliografia
Vydané v:Proceedings of the National Academy of Sciences - PNAS Ročník 121; číslo 39; s. e2409417121
Hlavní autori: Craig, William, van Ittersum, Jan-Willem, Ono, Ken
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: United States 24.09.2024
Predmet:
partitions
quasimodular forms
primes
ISSN:1091-6490, 1091-6490
On-line prístup:Zistit podrobnosti o prístupe
Tagy: Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
Popis
Shrnutí:We show that integer partitions, the fundamental building blocks in additive number theory, detect prime numbers in an unexpected way. Answering a question of Schneider, we show that the primes are the solutions to special equations in partition functions. For example, an integer ≥ 2 is prime if and only if [Formula: see text]where the [Formula: see text] are MacMahon's well-studied partition functions. More generally, for MacMahonesque partition functions [Formula: see text] we prove that there are infinitely many such prime detecting equations with constant coefficients, such as [Formula: see text].
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:1091-6490
1091-6490
DOI:10.1073/pnas.2409417121