Under what conditions does a secondary name server request a zone transfer from a primary name server?

When the primary SOA serial number is higher than the secondary's serial number, the secondary recognizes its zone data is stale and initiates an AXFR or IXFR zone transfer to synchronize. The SOA serial number is incremented on the primary each time the zone is modified, and the secondary compares serials during periodic refresh checks to detect when updates are needed.

If the secondary SOA serial were higher than the primary's, no transfer would be needed because the secondary would already have data at least as current as the primary.

A primary name server restart does not push or directly signal a zone transfer to secondary servers - the secondary is responsible for polling and comparing serial numbers.

A secondary server restart causes it to query the primary and compare SOA serials, but the actual trigger for the transfer is the serial number discrepancy, not the restart event itself.

TTL expiration causes a resolver to discard a cached record and re-query, which is a caching mechanism unrelated to authoritative zone transfer synchronization.