{"paper":{"title":"Generalized Hardy's identity for the astroid-type p-circle lattice point problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Masaya Kitajima","submitted_at":"2025-06-03T19:25:17Z","abstract_excerpt":"Let $r$ be a positive real number and $p$ satisfy $(2/p)\\in\\mathbb{N}$. Then, we consider the lattice point problem of the closed curves astroid-type $p$-circle $\\{x\\in\\mathbb{R}^{2}|\\ |x_{1}|^{p}+|x_{2}|^{p}=r^{p}\\}$ which generalize the circle. In investigating the asymptotic behavior of the error term in the area approximation of the circle, G.H. Hardy conjectured an infimum for the evaluation in 1917. One of the grounds for this conjecture is the Hardy's identity, which is a series representation of the term, consisting of the Bessel function of order one and a certain number-theoretic fun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.03331","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.03331/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}