On Invariants and the Theory of NumbersOf 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. |
Common terms and phrases
a₁ a₂ absolute invariant adoo American Mathematical Society apex b₁ b₂ binary form binary quadratic form c₁ characterize the classes classes of forms coefficients of 2"x3 coefficients of determinant coefficients taken modulo completely characterize congruent degree determinant unity discriminant divisible edition F₁ factor form 57 form a fundamental form f form qm formal invariant fundamental system given Hence integers integral coefficients taken invariant of F irregular covariant k₁ Lecture linear combination linear covariant linear function linear transformations linearly independent modular forms MODULAR GROUP modular invariants modular seminvariants multiplied obtain P₁ polynomial quadratic non-residue quadratic residue rational integral function rational integral invariants rational integral seminvariants real inflexion point real points real root replace S₁ seminvariants of F3 set of linearly system of forms system of modular Unabridged republication unaltered vanishes variables variant zero modulo