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As and application, we find a new period condition for two such $L$ functions to have a pole simultaneously. This points to an intriguing connection between a Fourier coefficient of a residual representation on $GSO(12)$ and a theta function on $\\widetilde{Sp}(16).$ A similar integral on $GSO(18)$ fails to unfold completely"},"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":"1505.01045","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-05-05T15:35:32Z","cross_cats_sorted":[],"title_canon_sha256":"a8f65863e885606192bf6027a5884d02b9b8876523ea6fbdf55b1d3609aeced4","abstract_canon_sha256":"1548328089df4e61c1fcbbd7f82b17106bf414dfb37749ef164148ff23715c37"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:16:52.085878Z","signature_b64":"7xhFn85crWZNmLie4cC+q475/mMctE18mKkXYwpZ9wnPoIeWein9wOwP7H7YBFblh7rDS0lrSgJq6OOBirTaCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc8227e6e029eb6e733941f106aa6e741b7f3aa14d91c044f90a9698f0139b17","last_reissued_at":"2026-05-18T02:16:52.085198Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:16:52.085198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Multi-variable Rankin-Selberg Integral for a Product of $GL_2$-twisted Spinor $L$-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Joseph Hundley, Xin Shen","submitted_at":"2015-05-05T15:35:32Z","abstract_excerpt":"We consider a new integral representation for $L(s_1, \\Pi \\times \\tau_1) L(s_2, \\Pi \\times \\tau_2),$ where $\\Pi$ is a globally generic cuspidal representation of $GSp_4,$ and $\\tau_1$ and $\\tau_2$ are two cuspidal representations of $GL_2$ having the same central character. 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