{"paper":{"title":"The Harris-Venkatesh conjecture for derived Hecke operators II: a unified Stark conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Robin Zhang","submitted_at":"2023-05-15T18:53:43Z","abstract_excerpt":"We prove a compatibility theorem between the Stark conjecture and the Harris-Venkatesh conjecture for imaginary dihedral modular forms of weight $1$. The key technical input is a general two-variable $\\mathrm{PGL}_2$ Siegel-Weil formula that precisely gives the Laurent series coefficients of Eisenstein series as a dual theta lift of Eisenstein series. This two-variable Siegel-Weil formula is applied to Rankin-Selberg periods of imaginary dihedral optimal forms and a refinement of Stark's formula relating $L$-values with elliptic units, yielding compatibility between derived Hecke operators and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.08956","kind":"arxiv","version":4},"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/2305.08956/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"}