An invitation to additive prime number theory

Abstract

The main purpose of this survey is to introduce an inexperienced reader to additive prime number theory and some related branches of analytic number theory. We state the main problems in the field, sketch their history and the basic machinery used to study them, and try to give a representative sample of the directions of current research.

References in corpus (2)

• Mean values of Dirichlet polynomials and applications to linear equations with prime variables
• The primes contain arbitrarily long arithmetic progressions

Cited by in corpus (7)

• Generalising the Hardy-Littlewood Method for Primes
• Small prime solutions to cubic Diophantine equations
• Diophantine equations in semiprimes
• Obstructions to uniformity, and arithmetic patterns in the primes
• Waring problem with the Ramanujan $\tau$-function
• Elementary Primes Counting Methods
• On Waring-Goldbach Problem for Squares, Cubes and Higher Powers