Extremal bounds for Dirichlet polynomials with random multiplicative coefficients

2022/04/07 by Benatar, Jacques, Nishry, Alon · 1 citation
#FOS: Mathematics #Number Theory (math.NT) #Probability (math.PR)

paper · doi:10.48550/arxiv.2204.03519

Abstract

For X(n) a Steinhaus random multiplicative function, we study the maximal size of the random Dirichlet polynomial D_N(t) = \frac1√(N) ∑_{n ≤ N} X(n) n^it, with t in various ranges. In particular, for fixed C>0 and any small ε>0 we show that, with high probability, exp( (log N)^1/2-ε ) ≪ sup_{|t| ≤ N^C} |D_N(t)| ≪ exp( (log N)^1/2+ε).

Cited by

• Large values of Dirichlet polynomials with multiplicative coefficients

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