Additive evaluations of the number of divisors
If m and n are positive integers, then a m ( n ) denotes the number of the parts congruent to 0 modulo m in all the partitions of n . On the strength of Euler’s pentagonal number theorem, this paper shows that the number of positive divisors of n can be expressed additively in terms of the partition...
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| Vydané v: | The Ramanujan journal Ročník 63; číslo 3; s. 583 - 601 |
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| Hlavný autor: | |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
New York
Springer US
01.03.2024
|
| Predmet: | |
| ISSN: | 1382-4090, 1572-9303 |
| On-line prístup: | Získať plný text |
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| Shrnutí: | If
m
and
n
are positive integers, then
a
m
(
n
)
denotes the number of the parts congruent to 0 modulo
m
in all the partitions of
n
. On the strength of Euler’s pentagonal number theorem, this paper shows that the number of positive divisors of
n
can be expressed additively in terms of the partition function
a
m
(
·
)
. |
|---|---|
| ISSN: | 1382-4090 1572-9303 |
| DOI: | 10.1007/s11139-023-00773-7 |