Abstract
In 2021 da Silva, Hirschhorn, and Sellers studied a wide variety of congruences for the k-elongated plane partition function dk(n) by various primes. They also conjectured the existence of an infinite congruence family modulo arbitrarily high powers of 2 for the function d7(n). We prove that such a congruence family exists - indeed, for powers of 8. The proof utilizes only classical methods, i.e. integer polynomial manipulations in a single function, in contrast to all other known infinite congruence families for dk(n) which require more modern methods to prove.
Original language | English (US) |
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Pages (from-to) | 267-282 |
Number of pages | 16 |
Journal | International Journal of Number Theory |
Volume | 20 |
Issue number | 1 |
DOIs | |
State | Published - Feb 1 2024 |
Bibliographical note
Publisher Copyright:© 2024 World Scientific Publishing Company.
Keywords
- Partition congruences
- Riemann surface
- infinite congruence family
- modular curve
- modular functions
- plane partitions