Short intervals asymptotic formulae for binary problems with primes and powers, I: density $3/2$

TL;DR

This paper establishes short interval asymptotic formulas for representing integers as sums of primes and squares, both assuming the Riemann Hypothesis and unconditionally, advancing understanding of prime and power representations.

Contribution

It provides new short interval asymptotic formulas for binary problems involving primes and squares, with results valid under both RH and unconditional assumptions.

Findings

Asymptotic formulas hold in short intervals for prime-square representations

Results are valid assuming RH and unconditionally

Advances understanding of prime and power sum representations

Abstract

We prove that suitable asymptotic formulae in short intervals hold for the problems of representing an integer as a sum of a prime and a square, or a prime square. Such results are obtained both assuming the Riemann Hypothesis and in the unconditional case.