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

DNS zone transfers are triggered by comparing SOA (Start of Authority) serial numbers. When the secondary polls the primary and finds the primary's SOA serial is higher, it knows the zone data has been updated and requests a full (AXFR) or incremental (IXFR) zone transfer to synchronize records.

A higher secondary SOA serial would mean the secondary is ahead of the primary, which would not trigger a transfer - the secondary already has newer or equal data.

Restarting the primary name server does not by itself cause the secondary to initiate a zone transfer; the secondary relies on SOA comparison or NOTIFY messages.

When a secondary restarts, it may reload its local zone file or poll the primary, but a transfer only occurs if the SOA serial comparison reveals the primary is newer.

TTL (Time to Live) governs how long resolvers cache individual resource records, not the synchronization interval between primary and secondary name servers.