Extremal bounds for Dirichlet polynomials with random multiplicative coefficients

Jacques Benatar; Alon Nishry

doi:10.4064/sm220829-6-3

Extremal bounds for Dirichlet polynomials with random multiplicative coefficients

Jacques Benatar, Alon Nishry

School of Mathematical Sciences

University of Helsinki

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

For X(n) a Steinhaus random multiplicative function, we study the maximal size of the random Dirichlet polynomial (Figure Presented) with t in various ranges. In particular, for fixed C > 0 and any small ε > 0 we show that, with high probability, exp (Figure Presented).

Original language	English
Pages (from-to)	59-80
Number of pages	22
Journal	Studia Mathematica
Volume	272
Issue number	1
DOIs	https://doi.org/10.4064/sm220829-6-3
State	Published - 2023

Keywords

Dirichlet polynomials
divisor sums
random multiplicative functions

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10.4064/sm220829-6-3

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title = "Extremal bounds for Dirichlet polynomials with random multiplicative coefficients",

abstract = "For X(n) a Steinhaus random multiplicative function, we study the maximal size of the random Dirichlet polynomial (Figure Presented) with t in various ranges. In particular, for fixed C > 0 and any small ε > 0 we show that, with high probability, exp (Figure Presented).",

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AU - Nishry, Alon

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PY - 2023

Y1 - 2023

N2 - For X(n) a Steinhaus random multiplicative function, we study the maximal size of the random Dirichlet polynomial (Figure Presented) with t in various ranges. In particular, for fixed C > 0 and any small ε > 0 we show that, with high probability, exp (Figure Presented).

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KW - Dirichlet polynomials

KW - divisor sums

KW - random multiplicative functions

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Extremal bounds for Dirichlet polynomials with random multiplicative coefficients

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