Abstract
We consider convolutions of divisor functions in arbitrary length with modular congruence restrictions, and introduce the notion of a space of convolution identities over the rational numbers. As a main result, we introduce a conjecture on the connection between the dimension of the space of convolution identities and the number of partitions of a positive integer into exactly three parts, and prove the conjecture for 15 cases. We also prove convolution identities in arbitrary length.
Original language | English |
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Pages (from-to) | 659-677 |
Number of pages | 19 |
Journal | Ramanujan Journal |
Volume | 54 |
Issue number | 3 |
DOIs | |
State | Published - Apr 2021 |
Keywords
- Convolution identities
- Convolution sums
- Elliptic functions
- Partitions into exactly k-parts