Integral and rational representations of forms

Date: 18/10/2023
Time: 14:00 - 15:30

Location: RISC, Hagenberg

Criteria are given for the integral representation of a binary quartic form by certain integral ternary quadratic forms and its rational representation by some discriminant forms. These conditions depend on integral or rational solutions of a Weierstrass equation associated to the forms. Usually I can give explicit constructions of solutions when they exist. Some computations are lengthy and were discovered, and are best verified, with the assistance of software.