On the a-points of derivatives of the Riemann zeta function

Tomokazu Onozuka

doi:10.1007/s40879-016-0124-2

On the a-points of derivatives of the Riemann zeta function

Tomokazu Onozuka

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

2 Citations (Scopus)

Abstract

We prove three results on the a-points of derivatives of the Riemann zeta function. The first result is a formula of the Riemann–von Mangoldt type; we estimate the number of a-points of derivatives of the Riemann zeta function. The second result is on certain exponential sum involving a-points. The third result is an analogue of the zero density theorem. We count the a-points of derivatives of the Riemann zeta function in 1/2-(loglogT)2/logT<Res<1/2+(loglogT)2/logT.

Original language	English
Pages (from-to)	53-76
Number of pages	24
Journal	European Journal of Mathematics
Volume	3
Issue number	1
DOIs	https://doi.org/10.1007/s40879-016-0124-2
Publication status	Published - Mar 1 2017
Externally published	Yes

All Science Journal Classification (ASJC) codes

Mathematics(all)

Access to Document

10.1007/s40879-016-0124-2

Cite this

@article{e45cc0cb5cff4eeeb497bc16fa2224fe,

title = "On the a-points of derivatives of the Riemann zeta function",

abstract = "We prove three results on the a-points of derivatives of the Riemann zeta function. The first result is a formula of the Riemann–von Mangoldt type; we estimate the number of a-points of derivatives of the Riemann zeta function. The second result is on certain exponential sum involving a-points. The third result is an analogue of the zero density theorem. We count the a-points of derivatives of the Riemann zeta function in 1/2-(loglogT)2/logT<Res<1/2+(loglogT)2/logT.",

author = "Tomokazu Onozuka",

note = "Publisher Copyright: {\textcopyright} 2016, Springer International Publishing AG.",

year = "2017",

month = mar,

day = "1",

doi = "10.1007/s40879-016-0124-2",

language = "English",

volume = "3",

pages = "53--76",

journal = "European Journal of Mathematics",

issn = "2199-675X",

publisher = "Springer International Publishing AG",

number = "1",

}

TY - JOUR

T1 - On the a-points of derivatives of the Riemann zeta function

AU - Onozuka, Tomokazu

PY - 2017/3/1

Y1 - 2017/3/1

N2 - We prove three results on the a-points of derivatives of the Riemann zeta function. The first result is a formula of the Riemann–von Mangoldt type; we estimate the number of a-points of derivatives of the Riemann zeta function. The second result is on certain exponential sum involving a-points. The third result is an analogue of the zero density theorem. We count the a-points of derivatives of the Riemann zeta function in 1/2-(loglogT)2/logT<Res<1/2+(loglogT)2/logT.

AB - We prove three results on the a-points of derivatives of the Riemann zeta function. The first result is a formula of the Riemann–von Mangoldt type; we estimate the number of a-points of derivatives of the Riemann zeta function. The second result is on certain exponential sum involving a-points. The third result is an analogue of the zero density theorem. We count the a-points of derivatives of the Riemann zeta function in 1/2-(loglogT)2/logT<Res<1/2+(loglogT)2/logT.

UR - http://www.scopus.com/inward/record.url?scp=85013188750&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85013188750&partnerID=8YFLogxK

U2 - 10.1007/s40879-016-0124-2

DO - 10.1007/s40879-016-0124-2

M3 - Article

AN - SCOPUS:85013188750

SN - 2199-675X

VL - 3

SP - 53

EP - 76

JO - European Journal of Mathematics

JF - European Journal of Mathematics

IS - 1

ER -

On the a-points of derivatives of the Riemann zeta function

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this