On Invariants and the Theory of Numbers (精装)

出版时间：2004-9  出版社：Dover Publications (2004年6月10日)  作者：Leonard Eugene Dickson  页数：110  

内容概要

Of enormous historical importance, this classic offered the first public formulation of Dickson's theory of invariants for modular forms and linear transformations. In many sections of the five lectures included here, Dickson aimed not at complete generality, but at an illumination of typical and suggestive topics. The introductory lecture is followed by sections on seminvariants of algebraic and modular binary forms; invariants of a modular group and formal invariants and covariants of modular forms; modular geometry and covariantive theory of a quadratic form in m variables, modulo 2; and a theory of plane cubic curves with a real inflexion point valid in ordinary and in modular geometry. 1914 ed.

书籍目录

INTRODUCTIONLECTURE IA THEORY OF INVARNTTS APPLICABLE TO ALGEBRAIC AND MODULAR FORMS  1-3.  Introduction to the algebraic side of the theory by means of the example of an algebraic quadratic form in m variables  4-7.  Introduction to the number theory side of the theory of invariants by means of the example of a modular quadratic form  8-9.  Modular invariants are rational and integral  10.  Characteristic modular invariants  11.  Number of linearly independent modular invariants  12.  Fundamental system of modular invariants  13.  Minor ro1e of modular covariants  14.  References to further developmentsLECTURE IISEMINVARIANTS OF ALGEBRAIC AND MODULAR BINARY FORMS  1-6.  Introductory example of the binary quartic form  7-10.  Fundamental system of modular seminvariants of a binary n-ic derived by induction from n - 1 to n  11.  Explicit fundamental system when the modulus  exceeds n  12.  Another method for the ease p > n  13.  Number of linearly independent seminvariants  14-15.  Derivation of modular invariants from semin-variantsLECTURE III INVARIANTS OF A MODULAR GROUP.  FORMAL INVARIANTS AND  COVARIANTS OF MODULAR FORMS.  APPLICATIONS  1-4.  Invariants of certain modular groups; problem of  Hurwitz  5-11.  Formal invariants and scminvariants of binary modular forms  12.  Theorem of Miss Sanderson  13.  Fundamental systems of modular covariants  14.  Form problem for the total binary modular group  15.  Invariantive classification of formsLECTURE IV MODULAR GEOMETRY AND COYARIANTIVE THEORY OF A QUAD  RATIC FORM IN m VARIABLES MODULO 2  1-2.  Introduction.  The polar locus  3.  Odd number of variables; apex; linear tangential equation  4.  Covariant line of a conic  5.  Even number of variables  6.  Covariant plane of a degenerate quadric surface   7.  A configuration defined by the quinary surface  8.  Certain formal and modular covariants of a conic  9-32.  Fundamental system of covariants of a conic  33.  References on modular geometryLECTURE V  A THEORY OF PLANE CUBIC CURVES WITH A REAL INFLEXION POIN VALID IN ORDINARY AND IN MODULARGEOMETRY

用户评论 (总计1条)

•   不变量这种思维方法，可以用在很多场合，看似复杂的东西，其实，都是万变不离其宗的，同样也可以演变成一种技巧。