On integers as the sum of a prime and a k-th power

2009/08/05 by Nayebi, Aran
#11D85 #11P32 #11P55 #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.0908.0554

Abstract

Let R_k(n) be the number of representations of an integer n as the sum of a prime and a k-th power. Define E_k(X) := |\n ≤ X, n ∈ I_k, nnot a sum of a prime and a k-th power\|. Hardy and Littlewood conjectured that for k = 2 and k=3, E_k(X) ≪_k 1. In this note we present an alternative approach grounded in the theory of Diophantine equations towards a proof of the conjecture for all k ≥ 2.

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