abelian extension abelian group absolute value algebraic integer algebraic number algebraic number field algebraic structure analytic number theory arithmetic arithmetic function artin reciprocity law cambridge university press class field theory class number formula complex number computational number theory continued fraction cyclic group dedekind domain diophantine approximation diophantine equation equivalence class factorization field extension finitely generated abelian group fundamental theorem of arithmetic galois extension galois group galois module galois theory geometry of numbers graduate texts in mathematics group cohomology group representation ideal class group integer irrational number l-function list of number theory topics list of recreational number theory topics mathematical reviews mathematics modular arithmetic number number theory prime ideal prime number prime power principal ideal quadratic form rank of an abelian group rational number ring homomorphism ring of integers transcendence theory transcendental number trivial group unique factorization domain