The quaternary Piatetski-Shapiro inequality with one prime of the form p=x²+y²+1

2020/12/07 by S. I. Dimitrov, Dimitrov, S. I.
Mathematics · #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2012.06476

openalex publication_date 2020/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we show that, for any fixed 10, the diophantine inequality |p₁^c+p₂^c+p₃^c+p₄^c-N|lt;ε has a solution in prime numbers p₁, p₂, p₃, p₄, such that p₁=x² + y² +1.

Related

• A quinary diophantine inequality by primes with one of the form p=x²+y²+1
• A ternary diophantine inequality by primes with one of the form p=x²+y²+1
• A quaternary diophantine inequality by prime numbers of a special type
• A ternary diophantine inequality by primes near to squares
• A hybrid of two theorems of Piatetski-Shapiro