Year: 2026
Type: article
Abstract: In 1988, Andrews Dyson and Hickerson showed that a [Formula: see text]-series [Formula: see text] found in Ramanujan’s lost notebook and related to partitions could be interpreted as counting ideals in [Formula: see text], and found similar formulas for [Formula: see text] in terms of ideals of [Formula: see text] and [Formula: see text]. Cohen followed this by showing more generally that for certain triples of quadratic fields, there is abelian extension and conductor so that the ray class character theta series for all three fields coincide. In the intervening years, several [Formula: see text]-series counting ideals in quadratic fields have been explored, nearly all relating to the fields explored by Andrews et al. In this paper, we give an example of a ray class character theta series which stems from [Formula: see text], [Formula: see text], and [Formula: see text]. We use recent work of Okano to give explicit formulas via quadratic form theta series with congruence conditions stemming from each field. We isolate an analogue of [Formula: see text] for this series and show that it has coefficients also given by a partition generating function.
Author: Lucas Perryman-Deskins
Institution: Oregon State University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G9000357359
OpenAlex ID: W4414460444
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