Prime Values of Quadratic Polynomials

2020/08/31 by N. A. Carella, Carella, N. A.
Mathematics · #2020: Primary 11N32 #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #General Mathematics (math.GM) #Secondary 11N05

paper · pdf · doi:10.48550/arxiv.2009.00417

openalex publication_date 2020/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This note investigates the prime values of the polynomial f(t)=qt²+a for any fixed pair of relatively prime integers a≥ 1 and q≥ 1 of opposite parity. For a large number x≥1, an asymptotic result of the form ∑_{n≤ x^1/2, n odd}Λ(qn²+a)≫ qx^1/2/2φ(q) is achieved for q≪ (log x)^b, where b≥ 0 is a constant.

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