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In this paper we prove nontrivial upper bounds for the average of $h_\\ell(-d)$ for all primes $\\ell \\geq 7$, as well as nontrivial upper bounds for certain higher moments for all primes $\\ell \\geq 3$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1409.3177","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-09-10T18:30:08Z","cross_cats_sorted":[],"title_canon_sha256":"b8d935c9a26ca7237d94e52e8c2f333e98661158e55abf8591cd2838214f3883","abstract_canon_sha256":"cd7e86a482ed782cb12947ad92c5cb16638a8a54445eb3491b7f859327ff48bc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:08.542109Z","signature_b64":"DWU09WqFafUydw2cjuU16EV8T4KL5r+ZSjni03a4SaNhrYD/VmN4+pHlXy2/FXgyS7B0qoLMe6YbkzWQ/7YyAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"199146288f1ae70e50e012fea778ca82999c341d7859e5e3e1c286845fc3248e","last_reissued_at":"2026-05-18T00:41:08.541428Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:08.541428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Averages and moments associated to class numbers of imaginary quadratic fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"D. 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