totally real number field造句

• The totally real number fields play a significant special role in algebraic number theory.
• Let F be a totally real number field and A a quaternion algebra over F satisfying the following conditions.
• This was proved by for "'Q "', and for all totally real number fields by.
• On the other hand there are still some arithmetic constraints on the Veech group of a Veech surface : for example its trace field must be a totally real number field.
• An arithmetic Fuchsian group is constructed from the following data : a totally real number field F, a quaternion algebra A over F and an order \ mathcal O in A.
• These days these are associated to algebraic groups ( respectively the Weil restriction from a totally real number field of, and the symplectic group ), for which it happens that automorphic representations can be derived from analytic functions.
• "' Hilbert modular forms "'are functions in " n " variables, each a complex number in the upper half-plane, satisfying a modular relation for 2 & times; 2 matrices with entries in a totally real number field.
• The first order zero conjectures are used in recent versions of the PARI / GP computer algebra system to compute Hilbert class fields of totally real number fields, and the conjectures provide one solution to Hilbert's twelfth problem, which challenged mathematicians to show how class fields may be constructed over any number field by the methods of complex analysis.