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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Bibliographic Details
Published in:The Ramanujan journal 2024-03, Vol.63 (3), p.583-601
Main Author: Merca, Mircea
Format: Article
Language:English
Subjects:
Combinatorics
Field Theory and Polynomials
Fourier Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Number Theory
Partitions (mathematics)
Citations: Items that this one cites
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Summary: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