Small Prime kth Power Residues and Nonresidues in Arithmetic Progressions

2024/05/21 by N. A. Carella, Carella, N. A.
Mathematics · #Analytic Number Theory Research #History and Theory of Mathematics #Mathematical and Theoretical Analysis

paper · pdf · doi:10.48550/arxiv.2405.13159

Abstract

Let p be a large odd prime, let x=log p)(loglog p)^3+ε and let q≪loglog p be an integer, where ε>0 is a small number. This note proves the existence of small prime quadratic residues and small prime quadratic nonresidues in the arithmetic progression a+qm≪ x, with relatively prime 1≤ a

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