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

2 Scopus citations

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

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

Access to Document

10.1016/j.jmaa.2017.12.045

Cite this

@article{00948e95ac104b73b9803536f107ab01,

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.",

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

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier Inc.",

year = "2018",

month = may,

day = "15",

doi = "10.1016/j.jmaa.2017.12.045",

language = "English (US)",

volume = "461",

pages = "1771--1785",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

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.

UR - http://www.scopus.com/inward/record.url?scp=85039973469&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85039973469&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2017.12.045

DO - 10.1016/j.jmaa.2017.12.045

M3 - Article

AN - SCOPUS:85039973469

SN - 0022-247X

VL - 461

SP - 1771

EP - 1785

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this