Zeros of normalized combinations of ξ(k)(s) on Re(s)=1/2

Sneha Chaubey; Amita Malik; Nicolas Robles; Alexandru Zaharescu

doi:10.1016/j.jmaa.2017.12.045

Zeros of normalized combinations of ξ^(k)(s) on Re(s)=1/2

Sneha Chaubey, Amita Malik, Nicolas Robles, Alexandru Zaharescu

Mathematics

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

Abstract

We consider functions of the form F_c→,a,T(s)=∑_j=0 ^M[Formula presented]ξ^(a+2j)(s), with L=log⁡[Formula presented] and c_j real constants satisfying a certain constraint. We show that as T→∞ the proportion of zeros of F_c→,a,T(s) on the critical line Re(s)=1/2 tends to 1.

Original language	English (US)
Pages (from-to)	1771-1785
Number of pages	15
Journal	Journal of Mathematical Analysis and Applications
Volume	461
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2017.12.045
State	Published - May 15 2018

Keywords

Critical line
Mollifier
Normalized combinations
Proportion
Riemann ξ-function
Zeros

ASJC Scopus subject areas

Analysis
Applied Mathematics

Online availability

10.1016/j.jmaa.2017.12.045

Library availability

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Cite this

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title = "Zeros of normalized combinations of ξ(k)(s) on Re(s)=1/2",

abstract = "We consider functions of the form Fc→,a,T(s)=∑j=0 M[Formula presented]ξ(a+2j)(s), with L=log⁡[Formula presented] and cj real constants satisfying a certain constraint. We show that as T→∞ the proportion of zeros of Fc→,a,T(s) on the critical line Re(s)=1/2 tends to 1.",

keywords = "Critical line, Mollifier, Normalized combinations, Proportion, Riemann ξ-function, Zeros",

author = "Sneha Chaubey and Amita Malik and Nicolas Robles and Alexandru Zaharescu",

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T1 - Zeros of normalized combinations of ξ(k)(s) on Re(s)=1/2

AU - Chaubey, Sneha

AU - Malik, Amita

AU - Robles, Nicolas

AU - Zaharescu, Alexandru

PY - 2018/5/15

Y1 - 2018/5/15

N2 - We consider functions of the form Fc→,a,T(s)=∑j=0 M[Formula presented]ξ(a+2j)(s), with L=log⁡[Formula presented] and cj real constants satisfying a certain constraint. We show that as T→∞ the proportion of zeros of Fc→,a,T(s) on the critical line Re(s)=1/2 tends to 1.

AB - We consider functions of the form Fc→,a,T(s)=∑j=0 M[Formula presented]ξ(a+2j)(s), with L=log⁡[Formula presented] and cj real constants satisfying a certain constraint. We show that as T→∞ the proportion of zeros of Fc→,a,T(s) on the critical line Re(s)=1/2 tends to 1.

KW - Critical line

KW - Mollifier

KW - Normalized combinations

KW - Proportion

KW - Riemann ξ-function

KW - Zeros

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