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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.30618","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-06-29T17:52:18Z","cross_cats_sorted":[],"title_canon_sha256":"76495d3acb4a26e10a1f5f6e7a06b87e7de88493371307d6438e8513aa092ab0","abstract_canon_sha256":"d58d06dd96cccfe279436e1233c79424fa149104eee3032508db10f2f8d0fa72"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T02:18:23.033935Z","signature_b64":"ZOQkUESJttYUv+IXlMpQO85t09/FeaBLRq96cs3pFQiwBmLmL5RNnx8hqgC7RUDSwmjvQGY4BXAA0Ur6OnsqDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac689eb9b9a631b7c8a2546fab98221b82d2b334823a6e7bb6366f5861245ea3","last_reissued_at":"2026-06-30T02:18:23.033484Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T02:18:23.033484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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