{"paper":{"title":"Analytic properties of the structure function for the one-dimensional one-component log-gas","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat","authors_text":"B. Jancovici, D.S. McAnally, P.J. Forrester","submitted_at":"2000-02-03T21:11:05Z","abstract_excerpt":"The structure function $S(k;\\beta)$ for the one-dimensional one-component log-gas is the Fourier transform of the charge-charge, or equivalently the density-density, correlation function. We show that for $|k| < {\\rm min}\n  (2\\pi \\rho, 2 \\pi \\rho \\beta)$, $S(k;\\beta)$ is simply related to an analytic function $f(k;\\beta)$ and this function satisfies the functional equation $f(k;\\beta) = f(-2k/\\beta;4/\\beta)$. It is conjectured that the coefficient of $k^j$ in the power series expansion of $f(k;\\beta)$ about $k=0$ is of the form of a polynomial in $\\beta/2$ of degree $j$ divided by $(\\beta/2)^j"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0002060","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"}