Kneser's method of neighbors

TL;DR

This paper surveys Kneser's 1957 method for enumerating classes in the genus of definite quadratic forms, highlighting its theoretical significance and practical applications in number theory.

Contribution

It provides a comprehensive overview of Kneser's method of neighbors and discusses its various applications in number theory.

Findings

Kneser's method effectively enumerates classes in quadratic form genera.

The method has significant theoretical and practical implications.

Applications include class number computations and form classification.

Abstract

In a landmark paper published in 1957, Kneser introduced a method for enumerating classes in the genus of a definite, integral quadratic form. This method has been deeply influential, on account of its theoretical importance as well as its practicality. In this survey, we exhibit Kneser's method of neighbors and indicate some of its applications in number theory.