{"paper":{"title":"Value distribution for the derivatives of the logarithm of $L$-functions from the Selberg class in the half-plane of absolute convergence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"{\\L}ukasz Pa\\'nkowski, Takashi Nakamura","submitted_at":"2015-01-09T05:34:32Z","abstract_excerpt":"In the present paper, we show that, for every $\\delta>0$, the function $(\\log {\\mathcal{L}}(s))^{(m)}$, where $m\\in {\\mathbb{N}} \\cup \\{ 0\\}$ and ${\\mathcal{L}} (s) := \\sum_{n=1}^\\infty a(n) n^{-s}$ is an element of the Selberg class ${\\mathcal{S}}$, takes any value infinitely often in any strip $1<\\Re(s) <1+\\delta$, provided $\\sum_{p\\leq x} |a (p)|^2 \\sim \\kappa\\pi(x)$ for some $\\kappa>0$. In particular, ${\\mathcal{L}} (s)$ takes any non-zero value infinitely often in the strip $1<\\Re(s)<1+\\delta$, and the first derivative of ${\\mathcal{L}} (s)$ vanishes infinitely often."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02045","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"}