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  2. Diophantine approximation - Wikipedia

    en.wikipedia.org/wiki/Diophantine_approximation

    Diophantine approximation. In number theory, the study of Diophantine approximation deals with the approximation of real numbers by rational numbers. It is named after Diophantus of Alexandria. The first problem was to know how well a real number can be approximated by rational numbers. For this problem, a rational number p / q is a "good ...

  3. Number theory - Wikipedia

    en.wikipedia.org/wiki/Number_theory

    t. e. Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." [1]

  4. Transcendental number theory - Wikipedia

    en.wikipedia.org/wiki/Transcendental_number_theory

    Noncommutative algebra. v. t. e. Transcendental number theory is a branch of number theory that investigates transcendental numbers (numbers that are not solutions of any polynomial equation with rational coefficients), in both qualitative and quantitative ways.

  5. Geometry of numbers - Wikipedia

    en.wikipedia.org/wiki/Geometry_of_numbers

    Geometry of numbers is the part of number theory which uses geometry for the study of algebraic numbers. Typically, a ring of algebraic integers is viewed as a lattice in and the study of these lattices provides fundamental information on algebraic numbers. [1] The geometry of numbers was initiated by Hermann Minkowski (1910). The geometry of ...

  6. Hardy–Ramanujan–Littlewood circle method - Wikipedia

    en.wikipedia.org/wiki/Hardy–Ramanujan...

    Hardy–Ramanujan–Littlewood circle method. In mathematics, the Hardy–Ramanujan–Littlewood circle method is a technique of analytic number theory. It is named for G. H. Hardy, S. Ramanujan, and J. E. Littlewood, who developed it in a series of papers on Waring's problem.

  7. Elliott–Halberstam conjecture - Wikipedia

    en.wikipedia.org/wiki/Elliott–Halberstam...

    Elliott–Halberstam conjecture. In number theory, the Elliott–Halberstam conjecture is a conjecture about the distribution of prime numbers in arithmetic progressions. It has many applications in sieve theory. It is named for Peter D. T. A. Elliott and Heini Halberstam, who stated a specific version of the conjecture in 1968.

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