Duke.txt

File contents

Computer Algebra and Applications Seminar

Title: Integral and rational representations of forms

Speaker: Prof. William Duke, UCLA Mathematics, U.S.A.

Time and Location:
Wed, October 18, 2023, 2 p.m.;
RISC Seminarroom, Castle of Hagenberg


Abstract:
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.