transcendental number theory
A branch of number theory dealing with transcendental numbers and their properties.
Transcendental number theory is a field that studies the properties of numbers that are not algebraic.
数論 (number theory) is the broader field; 超越数論 specifically focuses on transcendental numbers.
超越数 (transcendental number) is the object of study; 超越数論 is the theory about such numbers.
Compound of 超越 (transcendental) + 数 (number) + 論 (theory). A straightforward calque from English 'transcendental number theory'.