{"paper":{"title":"On Evaluation of Riesz Constants for Systems of Shifted Gaussians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"E.A. Kiselev, I.Ya. Novikov, L.A. Minin, S.M. Sitnik","submitted_at":"2013-08-12T19:10:31Z","abstract_excerpt":"In this paper we study single-parametric systems of integer shifts of Gauss and Lorenz functions. In case of Cauchy--Lorenz system we explicitly calculate nod functions and prove that it tends to sinc function in limit. For both Gauss and Cauchy--Lorenz systems and corresponding nod functions we explicitly calculate Riesz constants via trigonometric, hyperbolic and Jacobi theta-functions, also limit behavior of this values is found depending on parameters.\n  A special result is a sharp monotonicity property proved for a special ratio of Jacobi theta-functions which is important in many areas. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2649","kind":"arxiv","version":5},"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"}