Lower bounds for ζ(1+it) and GL(3)

Xiaoqing Li

doi:10.1007/s11139-025-01202-7

Lower bounds for ζ(1+it) and GL(3)

Xiaoqing Li

Mathematics

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

Abstract

We develop a soft method for deriving lower bounds for the Riemann zeta function on Re(s)=1 using the theory of GL(3) Eisenstein series.

Original language	English
Article number	43
Journal	Ramanujan Journal
Volume	68
Issue number	2
DOIs	https://doi.org/10.1007/s11139-025-01202-7
State	Published - Oct 2025

Keywords

Eisenstein series
Maass–Selberg relations
The Riemann zeta function

Access to Document

10.1007/s11139-025-01202-7

Cite this

@article{4f770ab16fe042fdb0425b53ad20b257,

title = "Lower bounds for ζ(1+it) and GL(3)",

abstract = "We develop a soft method for deriving lower bounds for the Riemann zeta function on Re(s)=1 using the theory of GL(3) Eisenstein series.",

keywords = "Eisenstein series, Maass–Selberg relations, The Riemann zeta function",

author = "Xiaoqing Li",

note = "Publisher Copyright: {\textcopyright} The Author(s) 2025.",

year = "2025",

month = oct,

doi = "10.1007/s11139-025-01202-7",

language = "English",

volume = "68",

journal = "Ramanujan Journal",

issn = "1382-4090",

publisher = "Springer Netherlands",

number = "2",

}

TY - JOUR

T1 - Lower bounds for ζ(1+it) and GL(3)

AU - Li, Xiaoqing

N1 - Publisher Copyright: © The Author(s) 2025.

PY - 2025/10

Y1 - 2025/10

N2 - We develop a soft method for deriving lower bounds for the Riemann zeta function on Re(s)=1 using the theory of GL(3) Eisenstein series.

AB - We develop a soft method for deriving lower bounds for the Riemann zeta function on Re(s)=1 using the theory of GL(3) Eisenstein series.

KW - Eisenstein series

KW - Maass–Selberg relations

KW - The Riemann zeta function

UR - https://www.scopus.com/pages/publications/105014816408

U2 - 10.1007/s11139-025-01202-7

DO - 10.1007/s11139-025-01202-7

M3 - Article

AN - SCOPUS:105014816408

SN - 1382-4090

VL - 68

JO - Ramanujan Journal

JF - Ramanujan Journal

IS - 2

M1 - 43

ER -

Lower bounds for ζ(1+it) and GL(3)

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this