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- W4382492092 abstract "Over the last century, a large variety of infinite congruence families have been discovered and studied, exhibiting a great variety with respect to their difficulty. Major complicating factors arise from the topology of the associated modular curve: classical techniques are sufficient when the associated curve has cusp count 2 and genus 0. Recent work has led to new techniques that have proven useful when the associated curve has cusp count greater than 2 and genus 0. We show here that these techniques may be adapted in the case of positive genus. In particular, we examine a congruence family over the 2-elongated plane partition diamond counting function $d_2(n)$ by powers of 7, for which the associated modular curve has cusp count 4 and genus 1. We compare our method with other techniques for proving genus 1 congruence families, and present a second congruence family by powers of 7 which we conjecture, and which may be amenable to similar techniques." @default.
- W4382492092 created "2023-06-29" @default.
- W4382492092 creator A5023334016 @default.
- W4382492092 creator A5051872698 @default.
- W4382492092 date "2023-06-27" @default.
- W4382492092 modified "2023-09-27" @default.
- W4382492092 title "2-Elongated Plane Partitions and Powers of 7: The Localization Method Applied to a Genus 1 Congruence Family" @default.
- W4382492092 doi "https://doi.org/10.48550/arxiv.2306.15594" @default.
- W4382492092 hasPublicationYear "2023" @default.
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