2015/06/10 by Karl Levy, Levy, Karl
Mathematics · #11B83 #11C08 #26C10 #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematical Dynamics and Fractals #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1506.03423
openalex publication_date 2015/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
What is the maximum possible value of the lead coefficient of a degree d polynomial Q(x) if |Q(1)|,|Q(2)|,…,|Q(k)| are all less than or equal to one? More generally we write Ld,[xk](x) for what we prove to be the unique degree d polynomial with maximum lead coefficient when bounded between 1 and -1 for x∈ [xk]=\x1,⋯,xk\. We calculate explicitly the lead coefficient of Ld,[xk](x) when d≤ 4 and the set [xk] is an arithmetic progression. We give an algorithm to generate Ld,[xk](x) for all d and [xk].