[bib]

@**techreport**{RISC6713,

author = {K. Banerjee and N.A. Smoot},

title = {{2-Elongated Plane Partitions and Powers of 7: The Localization Method Applied to a Genus 1 Congruence Family}},

language = {english},

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.},

number = {23-10},

year = {2023},

month = {August},

keywords = {Partition congruences, infinite congruence family, modular functions, plane partitions, partition analysis, modular curve, Riemann surface},

length = {35},

license = {CC BY 4.0 International},

type = {RISC Report Series},

institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},

address = {Altenberger Straße 69, 4040 Linz, Austria},

issn = {2791-4267 (online)}

}