2024/10/12 by Masahiro Mine, Mine, Masahiro
Mathematics · #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #Primary 11N32 #Secondary 11N25
paper · pdf · doi:10.48550/arxiv.2410.09558
openalex publication_date 2024/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove a new upper bound for the number of smooth values of a polynomial with integer coefficients. This improves Timofeev's previous result unless the polynomial is a product of linear polynomials with integer coefficients. As an application, we provide another proof for a result of Cassels which was used to prove that the Hurwitz zeta-function with algebraic irrational parameter has infinitely many zeros on the domain of convergence. We also apply the main result to a problem on primitive divisors of quadratic polynomials.