{"paper":{"title":"Shifted convolution sums of coefficients of symmetric power $L$-functions with $k$-full kernels over sums of squares in arithmetic progressions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Arnab Mitra, Jewel Mahajan","submitted_at":"2026-06-29T17:52:18Z","abstract_excerpt":"Let $q$ be an integer and let $f$ be a normalised Hecke eigenform of integral weight for the full modular group. Let $L(s,\\mathrm{sym}^j f)$ denote the $j$-th symmetric power $L$-function associated to $f$, and let $\\lambda_{\\mathrm{sym}^j f}(n)$ denote its $n$-th coefficient. We study the behaviour of the partial sum of $\\lambda_{\\mathrm{sym}^j f}(n)$, and of its second moment, taken over those sums of $m$ squares that are congruent to $1$ modulo $q$. As an application, we investigate the shifted convolution sum of $\\lambda_{\\mathrm{sym}^j f}(n)$ against a $k$-full kernel function, for any $k"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30618","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/2606.30618/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"}