Description
Online Number Theory Seminar
Abstract: In the 1850-s, Hermite introduced an equivalence relation for polynomials and showed that the polynomials of integer coefficients of given degree and discriminant fall apart in finitely many equivalence classes for this relation. Hermite's equivalence relation was apparently overlooked up to now. Much later, in 1972, Birch and Merriman showed that the integer polynomials of given degree and discriminant can be divided into finitely many GL2(Z)-equivalence classes. The result of Birch and Merriman is much deeper, based on a finiteness result for unit equations, which was not available to Hermite. In my talk, I will compare Hermite's equivalence relation with the much better known GL2(Z)-equivalence. As will be discussed, any two GL2(Z)-equivalent polynomials are equivalent in the sense of Hermite, whereas the converse is in general not true.
For access please contact the organizers (ntrg[at]science.unideb.hu).