Meaning of analytic number theory | Babel Free

Definitions

A branch of number theory that uses methods from mathematical analysis to solve problems about the integers.

uncountable

Equivalents

Examples

“1987, F. X. Gallagher, Applications of Guinand's Formula, A.C. Adolphson, A. Ghosh, J.B. Conrey, R.I. Yager (editors), Analytic Number Theory and Diophantine Problems: Proceedings of a Conference, Birkhäuser, page 135, According to Weil [22], analytic number theory, which deals with inequalities and asymptotic formulas, is not number theory but analysis.”

“2002, Chaohua Jia, Kohji Matsumoto (editors), Analytic Number Theory, Kluwer Academic, page ix, Talks covered various research fields including analytic number theory, algebraic number theory, modular forms and transcendental number theory.”

“Computational number theory, however, studies problems from elementary, algebraic geometric and analytic number theory which require the help of fast computers (particularly vector and parallel systems) and fast algorithms (particularly deterministic polynomial-time algorithms).”

CEFR level