Titlebook: Diophantine Equations and Power Integral Bases; Theory and Algorithm István Gaál Book 2019Latest edition Springer Nature Switzerland AG 201

Magnanimous

书目名称Diophantine Equations and Power Integral Bases影响因子(影响力)




书目名称Diophantine Equations and Power Integral Bases影响因子(影响力)学科排名




书目名称Diophantine Equations and Power Integral Bases网络公开度




书目名称Diophantine Equations and Power Integral Bases网络公开度学科排名




书目名称Diophantine Equations and Power Integral Bases被引频次




书目名称Diophantine Equations and Power Integral Bases被引频次学科排名




书目名称Diophantine Equations and Power Integral Bases年度引用




书目名称Diophantine Equations and Power Integral Bases年度引用学科排名




书目名称Diophantine Equations and Power Integral Bases读者反馈




书目名称Diophantine Equations and Power Integral Bases读者反馈学科排名

conference

Auxiliary Results and Tools,called . of type . (cf. Eq. (2.5)) with given algebraic ., ., where ., . are unknown units in a number field. These units are written as a power product of the generators of the unit group and the unknown exponents are to be determined. Baker’s method (Sect. 2.1) is used to give an initial upper bou

钳子

易受骗

Relative Thue Equations,d in effective form by Kotov and Sprindzuk (Dokl Akad Nauk BSSR 17:393–395, 477, 1973). This equation is a direct analogue of (.) in the relative case, when the ground ring is . instead of .. The equation given in this form has only finitely many solutions. Relative Thue equations are often consider

含糊其辞

The Resolution of Norm Form Equations,n of norm form equations was not investigated formerly. Our purpose is now to fill this gap and to give an efficient method for solving norm form equations under general conditions. The reason to include this algorithm in this book is that we use the same tools of Chap. . as for the above types of T

Alpha-Cells

Index Form Equations in General,n properties, makes the resolution of index form equations much easier. In the numerical examples the field . is often the composite of its subfields. This special case is considered in Sect. .. The general results on composite fields have several applications, see for example Sects. ., ., ., and ..

Alpha-Cells

灿烂

Quartic Fields,bles. The resolution of such an equation can yield a difficult problem. The main goal of this chapter is to point out that in the quartic case the index form equation can be reduced to a cubic and some corresponding quartic Thue equations (see Sect. .). This means that in fact the index form equatio

AVOW

Quintic Fields, quintic fields. In the most interesting case, for totally real quintic fields with Galois group .., .., or .., this computation takes several hours, contrary to the cubic and quartic cases, where to solve the index form equation was the matter of seconds or at most some minutes. The general method

Explosive

Sextic Fields,ds to calculate generators of power integral bases in case the sextic field admits some additional property, making the index form equation easier. We have efficient algorithms for sextic fields having quadratic or cubic subfields (see Sects. 11.2 and 11.3). Investigating the structure of the index