Conditional estimates for ▫$L$▫-functions in the Selberg class

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Title:	Conditional estimates for ▫$L$▫-functions in the Selberg class
Authors:	ID Palojärvi, Neea (Author) ID Simonič, Aleksander (Author)
Files:	RAZ_Palojarvi_Neea_2026.pdf (2,13 MB) MD5: 5FD5B98EBB705FED76ECFAF2654071A4 https://www.sciencedirect.com/science/article/pii/S0022314X26000338
Language:	English
Work type:	Article
Typology:	1.01 - Original Scientific Article
Organization:	FAMNIT - Faculty of Mathematics, Science and Information Technologies
Abstract:	We provide an explicit ▫$O\left(\log^{2}{T}\right)$▫-term of the celebrated Atkinson's formula for the error term of the second power moment of the Riemann zeta-function on the critical line. As an application, we obtain an explicit version of well-known estimate ▫$E(T)\ll_{\varepsilon}T^{\frac{1}{3}+\varepsilon}$▫.
Keywords:	Selberg class, Generalized Riemann hypothesis, Bandlimited functions
Publication version:	Version of Record
Publication date:	04.02.2026
Year of publishing:	2026
Number of pages:	str. 135-193
Numbering:	Vol. 285
PID:	20.500.12556/RUP-22652
UDC:	51
ISSN on article:	0022-314X
DOI:	10.1016/j.jnt.2025.12.014
COBISS.SI-ID:	268394243
Publication date in RUP:	13.02.2026
Views:	41
Downloads:	2
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Funder:	ARIS - Slovenian Research and Innovation Agency
Project number:	P1-0404-2019
Name:	Matematično modeliranje in enkripcija: od teoretičnih konceptov do vsakodnevnih aplikacij

License:	CC BY 4.0, Creative Commons Attribution 4.0 International

Link:	http://creativecommons.org/licenses/by/4.0/
Description:	This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Language:	Slovenian
Keywords:	Selbergov razred, posplošena Riemannova domneva, pasovno omejene funkcije

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