Nonholomorphic Ramanujan-type congruences for Hurwitz class numbers.
Where this comes from
- Record sourced from PubMed, PMID 32855297.
- Also identified by DOI 10.1073/pnas.2005984117 and PMC identifier 7486760.
- No licence information is recorded for this record.
- Because redistribution is not established, this page shows the abstract only. Follow the links below for the full text.
Abstract
In contrast to all other known Ramanujan-type congruences, we discover that Ramanujan-type congruences for Hurwitz class numbers can be supported on nonholomorphic generating series. We establish a divisibility result for such nonholomorphic congruences of Hurwitz class numbers. The two key tools in our proof are the holomorphic projection of products of theta series with a Hurwitz class number generating series and a theorem by Serre, which allows us to rule out certain congruences.