{"paper":{"title":"L-series and their 2-adic and 3-adic valuations at s=1 attached to CM elliptic curves","license":"","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Derong Qiu, Xianke Zhang","submitted_at":"2001-03-15T00:00:00Z","abstract_excerpt":"$L-$series attached to two classical families of elliptic curves with complex multiplications are studied over number fields, formulae for their special values at $s=1, $ bound of the values, and criterion of reaching the bound are given. Let $ E_1: y^{2}=x^{3}-D_1 x $ be elliptic curves over the Gaussian field $K=\\Q(\\sqrt{-1}), $ with $ D_1 =\\pi_{1} ... \\pi_{n} $ or $ D_1 =\\pi_{1} ^{2}... \\pi_{r} ^{2} \\pi_{r+1} ... \\pi_{n}$, where $\\pi_{1}, ..., \\pi_{n}$ are distinct primes in $K$. A formula for special values of Hecke $L-$series attached to such curves expressed by Weierstrass $\\wp-$function"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0103242","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":""},"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"}