The output of the following command will include adns1,2,3 if we are authoritative. If you get no answer, you have either typo'd the zone name or we are NOT authoritative.

Examples for which we are authoritative

[user@host]$ dig @adns1 doit.wisc.edu NS +short
adns2.doit.wisc.edu.
adns1.doit.wisc.edu.
adns3.doit.wisc.edu.

[user@host]$ dig @adns1 -x 144.92 NS +short
adns2.doit.wisc.edu.
adns3.doit.wisc.edu.
adns1.doit.wisc.edu.

Examples for which we are NOT authoritative

[user@host]$ dig @adns1 physics.wisc.edu NS +short
[user@host]$ dig @adns1 cs.wisc.edu NS +short
[user@host]$ dig @adns1 -x 128.105 NS +short
[user@host]$ 

Once you determine we are not authoritative, use dig to determine authority.

[user@host]$ dig cs.wisc.edu NS +short
dns2.cs.wisc.edu.
dns2.itd.umich.edu.
dns.cs.wisc.edu.
cs.wisc.edu.

[user@host]$ dig physics.wisc.edu NS +short
ns2.physics.wisc.edu.
dns.wiscnet.net.
dns.cs.wisc.edu.
ns1.physics.wisc.edu.

[user@host]$ dig -x 128.105 NS +short
dns2.cs.wisc.edu.
dns.cs.wisc.edu.
dns2.itd.umich.edu.
cs.wisc.edu.

Using WHOIS

This method can be used for second level domains and will work even if the authoritative DNS server is NOT correctly configured.

[user@host]$ whois wisconsin.edu  
..
..

Name Servers: 
   ADNS1.DOIT.WISC.EDU      
   ADNS2.DOIT.WISC.EDU      
   ADNS3.DOIT.WISC.EDU