On the number of pairs of positive integers x, y ≤ H such that x² + y² + 1 is squarefree

2010/07/02 by D. I. Tolev, Doychin Tolev, Tolev, Doychin · 1 citation
Computer Science · Mathematics · #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1007.0353

openalex publication_date 2010/07/02 · arxiv created 2010/09/10 · arxiv updated 2010/09/13 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

It is not difficult to find an asymptotic formula for the number of pairs of positive integers x, y ≤ H such that x² + y² + 1 is squarefree. In the present paper we improve the estimate for the error term in this formula using the properties of certain exponential sums. A.Weils's estimate for the Kloosterman sum plays the major role in our analysis.

Cited by

• Errata and Addenda to Mathematical Constants

Related

• On the number of pairs of positive integers x, y ≤ H such that x²+y²+1, x²+y²+2 are square-free
• Pairs of square-free values of the type n²+1, n²+2
• Square-free values of n²+n+1
• Three consecutive near-square squarefree numbers
• Pairs of k-free Numbers, consecutive square-full Numbers