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

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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.",

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.

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UR - https://www.scopus.com/pages/publications/85039973469#tab=citedBy

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

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