{"paper":{"title":"Arithmetic theory of E-operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.NT","authors_text":"Stephane Fischler (LM-Orsay), Tanguy Rivoal (IF)","submitted_at":"2014-06-23T17:31:17Z","abstract_excerpt":"In [S\\'eries Gevrey de type arithm\\'etique I Th\\'eor\\'emes de puret\\'e et de dualit\\'e, Annals of Math. 151 (2000), 705--740], Andr\\'e has introduced E-operators, a class of differential operators intimately related to E-functions, and constructed local bases of solutions for these operators. In this paper we investigate the arithmetical nature of connexion constants of E-operators at finite distance, and of Stokes constants at infinity. We prove that they involve values at algebraic points of E-functions in the former case, and in the latter one, values of G-functions and of derivatives of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5995","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"}