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Here $0<\\kappa\\leq 1$ is such that there are no (ITE) in the region $\\{\\lambda\\in {\\mathbb C}:\\: |{\\rm Im}\\:\\lambda|\\geq C(| {\\rm Re}\\:\\lambda|+1)^{1-\\frac{\\kappa}{2}}\\}$ for some $C>0$."},"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":"1403.3949","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-03-16T19:00:31Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"4b891ce3cc5ca9b6086428502ded606f1ccd015a97831e671510e2d04a985043","abstract_canon_sha256":"e2d8507b4e9a967023584619fdff8dc8e1d2eb7cb089c4a1136a88503644877b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:21.288209Z","signature_b64":"FXw5s3PA92Z2ii/AmWtdHp9qNJlCb2p5dyIUjJ+PjjjuP9FCeSr0NgsvBqHs+h12SdLCp8mcweY/bJ5qkUeiCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dfc09b33f1cb8867d3a8a33d4814503adfd5b43e85e3f21dd28e5436fc30661a","last_reissued_at":"2026-05-18T02:31:21.287503Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:21.287503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotics of the number of the interior transmission eigenvalues","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Georgi Vodev, Vesselin Petkov","submitted_at":"2014-03-16T19:00:31Z","abstract_excerpt":"We prove a Weyl asymptotics $N(r) = c r^d + {\\mathcal O}_{\\epsilon}(r^{d - \\kappa + \\epsilon})$, $\\forall\\, 0< \\epsilon \\ll 1$, for the counting function $N(r) = \\sharp\\{\\lambda_j \\in {\\mathbb C} \\setminus \\{0\\}:\\: |\\lambda_j| \\leq r^2\\}$, $r>1$, of the interior transmission eigenvalues (ITE), $\\lambda_j$. 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