Ramanujan congruences for Siegel modular forms
Michael Dewar, Olav K. Richter
TL;DR
This paper investigates conditions under which Ramanujan-type congruences occur for Jacobi and Siegel modular forms, providing new criteria and explicit examples of such congruences.
Contribution
It extends Ramanujan congruence results from Jacobi forms to Siegel modular forms of degree 2, including explicit examples.
Findings
Conditions for existence of Ramanujan-type congruences for Jacobi forms
Extension of these conditions to Siegel modular forms of degree 2
Explicit examples of Siegel modular forms satisfying Ramanujan-type congruences
Abstract
We determine conditions for the existence and non-existence of Ramanujan-type congruences for Jacobi forms. We extend these results to Siegel modular forms of degree 2 and as an application, we establish Ramanujan-type congruences for explicit examples of Siegel modular forms.
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Taxonomy
TopicsAdvanced Mathematical Identities · Advanced Algebra and Geometry · Analytic Number Theory Research