{"paper":{"title":"Symmetry of zeros of Lerch zeta-function for equal parameters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ram\\=unas Garunk\\v{s}tis, Rokas Tamo\\v{s}i\\=unas","submitted_at":"2019-01-30T12:53:04Z","abstract_excerpt":"For most values of parameters $\\lambda$ and $\\alpha$, the zeros of the Lerch zeta-function $L(\\lambda, \\alpha, s)$ are distributed very chaotically. In this paper we consider the special case of equal parameters $L(\\lambda, \\lambda, s)$ and show by calculations that the nontrivial zeros either lie extremely close to the critical line $\\sigma = 1/2$ or are distributed almost symmetrically with respect to the critical line. We also investigate this phenomenon theoretically."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.10790","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"}