automorphic
|au-to-mor-phic|
🇺🇸
/ˌɔːtəˈmɔːrfɪk/
🇬🇧
/ˌɔːtə(ʊ)ˈmɔːfɪk/
self-form / self-same form
Etymology
'automorphic' originates from Greek elements via New Latin and Modern English: from Greek 'autos' meaning 'self' and 'morphē' meaning 'form', combined as 'automorphos' and later adapted into New Latin/Modern English as 'automorphic'.
'automorphic' developed from Greek 'automorphos' → New/Modern Latin 'automorphicus' → English 'automorphic'.
Initially formed from elements meaning 'self' + 'form' (i.e. 'having the same or self form'), it came to be used in English for things related to automorphisms and, in specialized mathematics, to automorphic forms and invariant objects.
Meanings by Part of Speech
Adjective 1
relating to or produced by an automorphism; preserved or mapped into itself by a structure-preserving isomorphism (an automorphism).
The subgroup is automorphic in the larger group, so any automorphism of the group sends it to itself.
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Adjective 2
(Mathematics — number theory, representation theory) Pertaining to automorphic forms or automorphic representations; used of functions or forms invariant under the action of a discrete group.
Automorphic forms play a central role in modern number theory and the Langlands program.
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Adjective 3
(Recreational number theory) Describing a number whose powers (often the square) end with the number itself (an automorphic number).
25 is automorphic because 25^2 = 625 ends with 25.
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Last updated: 2025/11/27 06:40