Number Theory Seminar

Tuesday, January 17, 2023 11:30 am - 11:30 am EST

**Note this seminar will not be held at the usual time**

Yu-Ru Liu, Department of Pure Mathematics, University of Waterloo

"On the multidimensional Hilbert-Kamke problem"

Waring's problem is about representations of integers as sums of fixed powers, and Hilbert-Kamke's problem is about a system of Diophantine equations of Waring's type. Motivated by the asymptotic estimates for multidimensional Waring's problem, we consider multidimensional analogues of Hilbert-Kamke's problem. We proved that the corresponding singular series is bounded below by an absolute positive constant without any nonsingular local solubility assumption. The number of variables we need is near-optimal. This is joint work with Wentang Kuo and Xiaomei Zhao.

This seminar will be held online: