Student Number Theory Seminar

Samantha Nadia Pater, Cuiwen Zhu and Hanwu Zhou

The Hasse Principle for Diagonal Forms via the Circle Method

The Hasse principle predicts that a Diophantine equation should have a rational solution whenever it has solutions in reals and p-adics for all primes p. For diagonal forms, this principle can be analyzed via the Hardy–Littlewood circle method. In this talk, we examine how the major and minor arc contributions are handled to establish asymptotic formulas for the number of integral solutions. Moreover, we would present a sketch of Jorg Brudern and Trevor D. Wooley's proof of the Hasse principle for pairs of diagonal cubic forms in thirteen or more variables.

MC 5417