analytic number theory

analytic number theory

English

Noun

analytic number theory (uncountable)

1. (mathematics, number theory) A branch of number theory that uses methods from mathematical analysis to solve problems about the integers.
   • 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.

   • 2002, Song Y. Yan, Number Theory for Computing, Springer, 2nd Edition, page 174,

     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).

Coordinate terms

• algebraic number theory
• computational number theory
• geometry of numbers, geometric number theory

Derived terms

• abstract analytic number theory

Translations

branch of number theory

German: analytische Zahlentheorie f

Italian: teoria analitica dei numeri f

Further reading

• Diophantine equation on Wikipedia.Wikipedia
• Dirichlet series on Wikipedia.Wikipedia
• Prime number theorem on Wikipedia.Wikipedia
• Riemann zeta function on Wikipedia.Wikipedia