Comparison of the circle method applied to the Goldbach Problem and the Restricted Digit Problem

Abstract

The Hardy-Littlewood circle method is a widely used tool in the field of analytic number theory. James Maynard \cite{May} uses it to prove that there are infinitely many primes without a certain fixed digit in their decimal expansion. His application however is slightly different from the original approach. In this thesis the parallels and differences are discussed between the original circle method applied to the Ternary Goldbach Problem and the modified circle method applied to the Restricted Digit Problem. It is quite interesting that we can solve the Restricted Digit Problem, which is a binary problem, with the circle method. After all the Binary version of the Golbach Problem can not be solved with it.