{"paper":{"title":"Algebraic estimates, stability of local zeta functions, and uniform estimates for distribution functions","license":"","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"D. H. Phong, Jacob Sturm","submitted_at":"2000-07-01T00:00:00Z","abstract_excerpt":"A method of ``algebraic estimates'' is developed, and used to study the stability properties of integrals of the form \\int_B|f(z)|^{-\\d}dV, under small deformations of the function f. The estimates are described in terms of a stratification of the space of functions \\{R(z)=|P(z)|^{\\e}/|Q(z)|^{\\d}\\} by algebraic varieties, on each of which the size of the integral of R(z) is given by an explicit algebraic expression. The method gives an independent proof of a result on stability of Tian in 2 dimensions, as well as a partial extension of this result to 3 dimensions. In arbitrary dimensions, comb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0007202","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"}