2015/05/06 by Adam J. Harper, Harper, Adam J., Ashkan Nikeghbali +3 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Number Theory (math.NT) #Probability (math.PR) #math.CA #math.NT #math.PR
paper · pdf · doi:10.48550/arxiv.1505.01443
23 pages, to appear, "Analytic Number Theory" in honor of Helmut Maier's 60th birthday
arxiv created 2015/05/06 · openalex publication_date 2015/05/06 · arxiv updated 2015/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give lower bounds for the small moments of the sum of a random multiplicative function, which improve on some results of Bondarenko and Seip and constitute further progress towards (dis)proving a conjecture of Helson. We also prove asymptotics for the even integer moments. The latter have also been obtained very recently and independently by Heap and Lindqvist. Our proofs involve general lower bound techniques for random multiplicative functions, mean value results for multiplicative functions in several variables, and some calculations with Birkhoff polytopes.