Number Theory Seminar

Alan Talmage, Department of Pure Mathematics, University of Waterloo

"Prime Solutions of Systems of Diagonal Equations"

We present a result showing existence of prime solutions to systems of polynomial equations with sufficiently strong mean value bounds. This result serves to bring our knowledge of prime solutions of Diophantine systems closer to the state of our knowledge regarding integer solutions to such systems as new mean value bounds are proved. Results for Vinogradov systems and conditional results for the Waring-Goldbach problem for cubes will be presented as corollaries of this work.

MC 5417