On large values of the Riemann zeta-function on short segments of the critical line

Maxim A. Korolev. "On large values of the Riemann zeta-function on short segments of the critical line." Acta Arithmetica 166.4 (2014): 349-390. <http://eudml.org/doc/279175>.

@article{MaximA2014,
abstract = {We obtain a series of new conditional lower bounds for the modulus and the argument of the Riemann zeta function on very short segments of the critical line, based on the Riemann hypothesis. In particular, we prove that for any large fixed constant A > 1 there exist(non-effective) constants T₀(A) > 0 and c₀(A) > 0 such that the maximum of |ζ (0.5+it)| on the interval (T-h,T+h) is greater than A for any T > T₀ and h = (1/π)lnlnln\{T\}+c₀.},
author = {Maxim A. Korolev},
journal = {Acta Arithmetica},
keywords = {Riemann zeta function; argument of the Riemann zeta-function; Gram's law; critical line},
language = {eng},
number = {4},
pages = {349-390},
title = {On large values of the Riemann zeta-function on short segments of the critical line},
url = {http://eudml.org/doc/279175},
volume = {166},
year = {2014},
}

TY - JOUR
AU - Maxim A. Korolev
TI - On large values of the Riemann zeta-function on short segments of the critical line
JO - Acta Arithmetica
PY - 2014
VL - 166
IS - 4
SP - 349
EP - 390
AB - We obtain a series of new conditional lower bounds for the modulus and the argument of the Riemann zeta function on very short segments of the critical line, based on the Riemann hypothesis. In particular, we prove that for any large fixed constant A > 1 there exist(non-effective) constants T₀(A) > 0 and c₀(A) > 0 such that the maximum of |ζ (0.5+it)| on the interval (T-h,T+h) is greater than A for any T > T₀ and h = (1/π)lnlnln{T}+c₀.
LA - eng
KW - Riemann zeta function; argument of the Riemann zeta-function; Gram's law; critical line
UR - http://eudml.org/doc/279175
ER -