Explicit upper bound for an average number of divisors of quadratic\n polynomials

2015/09/28 by Kostadinka Lapkova, Lapkova, Kostadinka
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Mathematics and Applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1509.08243

openalex publication_date 2015/09/28 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

Consider the divisor sum \∑_{n\≤ N}\τ(n²+2bn+c) for integers b and\nc which satisfy certain extra conditions. For this average sum we obtain an\nexplicit upper bound, which is close to the optimal. As an application we\nimprove the maximal possible number of D(-1)-quadruples.\n

Citations

• An explicit density estimate for Dirichlet 𝐿-series

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