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Softcover ISBN:  9780821845981 
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Book DetailsColloquium PublicationsVolume: 4; 1914; 238 ppMSC: Primary 11; 32
Following the tradition of the American Mathematical Society, the seventh colloquium of the Society was held as part of the summer meeting that took place at the University of Wisconsin, in Madison. Two sets of lectures were presented: On Invariants and the Theory of Numbers, by L. E. Dickson, and Functions of Several Complex Variables, by W. F. Osgood.
Dickson considers invariants of quadratic forms, with a special emphasis on invariants of forms defined in characteristic \(p\), also called modular invariants, which have numbertheoretic consequences. He is able to find a fundamental set of invariants for both settings. For binary forms, Dickson introduces semiinvariants in the modular case, and again finds a fundamental set. These studies naturally lead to the important study of invariants of the standard action of the modular group. The lectures conclude with a study of “modular geometry”, which is now known as geometry over \(\mathbf{F}_p\).
The lectures by Osgood review the state of the art of several complex variables. At this time, the theory was entirely functiontheoretic. Already, though, Osgood can introduce the ideas and theorems that will be fundamental to the subject for the rest of the century: Weierstrass preparation, periodic functions and theta functions, singularities—including Hartogs' phenomenon, the boundary of a domain of holomorphy, and so on.
ReadershipGraduate students and research mathematicians interested in number theory and analysis.

Table of Contents

L. E. Dickson. On Invariants and the Theory of Numbers.

Introduction

Lecture I. A theory of invariants applicable to algebraic and modular forms

Lecture II. Seminvariants of algebraic and modular binary forms

Lecture III. Invariants of a modular group. Formal Invariants and covariants of modular forms. Applications

Lecture IV. Modular geometry and covariantive theory of a quadratic form in $m$ variables modulo 2

Lecture V. A theory of plane cubic curves with a real inflexion point valid in ordinary and in modular geometry

W. F. Osgood. Topics in the Theory of Functions of Several Complex Variables.

Lecture I. A General Survey of the Field

Lecture II. Some General Theorems

Lecture III. Singular Points and Analytic Continuation

Lecture IV. Implicit Functions

Lecture V. The Prime Function on an Algebraic Configuration


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Following the tradition of the American Mathematical Society, the seventh colloquium of the Society was held as part of the summer meeting that took place at the University of Wisconsin, in Madison. Two sets of lectures were presented: On Invariants and the Theory of Numbers, by L. E. Dickson, and Functions of Several Complex Variables, by W. F. Osgood.
Dickson considers invariants of quadratic forms, with a special emphasis on invariants of forms defined in characteristic \(p\), also called modular invariants, which have numbertheoretic consequences. He is able to find a fundamental set of invariants for both settings. For binary forms, Dickson introduces semiinvariants in the modular case, and again finds a fundamental set. These studies naturally lead to the important study of invariants of the standard action of the modular group. The lectures conclude with a study of “modular geometry”, which is now known as geometry over \(\mathbf{F}_p\).
The lectures by Osgood review the state of the art of several complex variables. At this time, the theory was entirely functiontheoretic. Already, though, Osgood can introduce the ideas and theorems that will be fundamental to the subject for the rest of the century: Weierstrass preparation, periodic functions and theta functions, singularities—including Hartogs' phenomenon, the boundary of a domain of holomorphy, and so on.
Graduate students and research mathematicians interested in number theory and analysis.

L. E. Dickson. On Invariants and the Theory of Numbers.

Introduction

Lecture I. A theory of invariants applicable to algebraic and modular forms

Lecture II. Seminvariants of algebraic and modular binary forms

Lecture III. Invariants of a modular group. Formal Invariants and covariants of modular forms. Applications

Lecture IV. Modular geometry and covariantive theory of a quadratic form in $m$ variables modulo 2

Lecture V. A theory of plane cubic curves with a real inflexion point valid in ordinary and in modular geometry

W. F. Osgood. Topics in the Theory of Functions of Several Complex Variables.

Lecture I. A General Survey of the Field

Lecture II. Some General Theorems

Lecture III. Singular Points and Analytic Continuation

Lecture IV. Implicit Functions

Lecture V. The Prime Function on an Algebraic Configuration