DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-08-29

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

The exponent of convergence of a zero sequence

Let $(a_{n})_{n \geq 1}$ be a sequence of nonzero complex numbers with no finite accumulation point. The exponent of convergence of $(a_{n})$ is

$λ : = \inf {s > 0 : \sum_{n \geq 1} ∣ a_{n} ∣^{- s} < \infty} \in [0, \infty] .$

Equivalently, $λ$ is the threshold between convergence and divergence of the reciprocal power sums.

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