{"paper":{"title":"Counterexamples of Friedlander--Iwaniec dual sums conjecture","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Khai-Hoan Nguyen-Dang","submitted_at":"2026-07-18T08:06:23Z","abstract_excerpt":"Let $a(n)$ and $b(n)$ be arithmetic sequences, and $$A(s)=\\sum_{n\\ge1}a(n)n^{-s}, \\qquad B(s)=\\sum_{n\\ge1}b(n)n^{-s},$$ be the two Dirichlet series related by a certain functional equation. Let $m$ be the \\emph{analytic degree} of the functional equation. For $x>0$ and a positive integer $N$, Friedlander and Iwaniec (2005) define the sharply truncated nonlinear dual sum $$\\mathcal B_{\\ell,D}(x,N) := \\sum_{\\substack{n\\in\\mathbb N\\\\ n\\le N}} b(n)n^{-\\beta_m} \\cos\\left( 2\\pi m\\left(\\frac{nx}{D}\\right)^{1/m} +\\frac{\\pi\\ell}{4} \\right),$$ where $D\\ge1$ is the conductor, $\\beta_m:=\\frac{m+1}{2m}$, a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16695","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.16695/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"}