{"paper":{"title":"Supersymmetry, differential operators of infinite order and theta functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Mikhail Kapranov","submitted_at":"2026-08-13T05:35:09Z","abstract_excerpt":"In 1972, M. Sato proposed an approach to proving modularity of forms like Thetanullwerte by characterizing them via certain differential operators of infinite order (DOI) in the modular variable(s) alone. A DOI is an infinite series in derivatives decreasing so fast that it acts on holomorphic functions by a sheaf morphism. This approach was developed by several authors including Kashiwara, Kawai, Takei and Yoshida.\n  We give an interpretation of this approach using supersymmetry which provides a natural source of DOIs: the naive exponential of any odd supersymmetry generator is a DOI. The cas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.12846","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.12846/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}