{"paper":{"title":"A generalized Kontsevich-Vishik trace for Fourier Integral Operators and the Laurent expansion of $\\zeta$-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.OA","math.SP"],"primary_cat":"math.AP","authors_text":"Simon Scott, Tobias Hartung","submitted_at":"2015-10-25T23:38:48Z","abstract_excerpt":"Based on Guillemin's work on gauged Lagrangian distributions, we will introduce the notion of a poly-$\\log$-homogeneous distribution as an approach to $\\zeta$-functions for a class of Fourier Integral Operators which includes cases of amplitudes with asymptotic expansion $\\sum_{k\\in\\mathbb{N}}a_{m_k}$ where each $a_{m_k}$ is $\\log$-homogeneous with degree of homogeneity $m_k$ but violating $\\Re(m_k)\\to-\\infty$. We will calculate the Laurent expansion for the $\\zeta$-function and give formulae for the coefficients in terms of the phase function and amplitude as well as investigate generalizatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07324","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":""},"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"}