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

Tel Aviv University

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

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

All Science Journal Classification (ASJC) codes

General Mathematics

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10.4064/sm220829-6-3

Cite this

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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).",

keywords = "Dirichlet polynomials, divisor sums, random multiplicative functions",

author = "Jacques Benatar and Alon Nishry",

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year = "2023",

doi = "10.4064/sm220829-6-3",

language = "الإنجليزيّة",

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T1 - Extremal bounds for Dirichlet polynomials with random multiplicative coefficients

AU - Benatar, Jacques

AU - Nishry, Alon

N1 - Publisher Copyright: © Instytut Matematyczny PAN, 2023.

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).

AB - 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).

KW - Dirichlet polynomials

KW - divisor sums

KW - random multiplicative functions

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U2 - 10.4064/sm220829-6-3

DO - 10.4064/sm220829-6-3

M3 - مقالة

SN - 0039-3223

VL - 272

SP - 59

EP - 80

JO - Studia Mathematica

JF - Studia Mathematica

IS - 1

ER -

Extremal bounds for Dirichlet polynomials with random multiplicative coefficients

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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