Algebraic and Analytic Number Theory

Branches that attack questions about the integers by borrowing the machinery of algebra and of analysis. An entry belongs here when its cited source describes number fields, rings of integers and ideals, or the use of zeta functions, complex integration and estimates to count primes and other arithmetic objects. It does not belong here when the branch deals with elementary arithmetic and congruences alone, which are covered by the elementary group. The group holds the modern core of number theory, from which most deep results of recent decades have come.