binary quadratic form造句
例句与造句
- Gauss proved that for every value " D ", there are only finitely many classes of binary quadratic forms with discriminant " D ".
- Using this property as the starting point for a theory of composition of binary quadratic forms Manjul Bhargava went on to define fourteen different composition laws using a cube.
- In April 1880, Markov defended his master's thesis " About Binary Quadratic Forms with Positive Determinant ", which was encouraged by Aleksandr Korkin and Yegor Zolotarev.
- This configuration was extensively used by Manjul Bhargava, an Indian-American Fields Medal winning mathematician, to study the composition laws of binary quadratic forms and other such forms.
- Properties of binary quadratic forms depend in an essential way on the nature of the coefficients, which may be real numbers, rational numbers, or in the most delicate case, integers.
- It's difficult to find binary quadratic form in a sentence. 用binary quadratic form造句挺难的
- In 1912, the University of Berlin awarded him a Ph . D . in mathematics, for a thesis, supervised by Landau, on the analytic number theory of binary quadratic forms.
- To each pair of opposite faces of a Bhargava cube one can associate an integer binary quadratic form thus getting three binary quadratic forms corresponding to the three pairs of opposite faces of the Bhargava cube.
- To each pair of opposite faces of a Bhargava cube one can associate an integer binary quadratic form thus getting three binary quadratic forms corresponding to the three pairs of opposite faces of the Bhargava cube.
- Arithmetical aspects of the theory of binary quadratic forms are related to the arithmetic of quadratic fields and have been much studied, notably, by Gauss in Section V of " Disquisitiones Arithmeticae ".
- The pair of binary quadratic forms ( ax ^ 2 + 2bxy + cy ^ 2, dx ^ 2 + 2exy + fy ^ 2 ) can be represented by a doubly symmetric Bhargava cube as in the figure.
- Gauss also considered a coarser notion of equivalence, under which the set of binary quadratic forms of a fixed discriminant splits into several genera of forms and each "'genus "'consists of finitely many classes of forms.
- The initial part of the Lagrange spectrum, namely the part lying in the interval [ & radic; 5, 3 ), is associated with some binary quadratic forms that are indefinite ( so factoring into two real linear forms ).
- Volume 1 on elementary and additive number theory includes the topics such as Dirichlet's theorem, Brun's sieve, binary quadratic forms, Goldbach's conjecture, Waring's problem, and the Hardy Littlewood work on the singular series.
- is an indefinite binary quadratic form with real coefficients and discriminant D = b ^ 2-4ac, then there are integers " x ", " y " for which " f " takes a nonzero value of absolute value at most
- Note that there is a close relation between reducing binary quadratic forms and continued fraction expansion; one step in the continued fraction expansion of a certain quadratic irrationality gives a unary operation on the set of reduced forms, which cycles through all reduced forms in one equivalence class.