An omega-result for Beurling generalized integers

An omega-result for Beurling generalized integers

We consider Beurling number systems with very well-behaved primes, in the sense that psi(x) = x + O(x(alpha)) for some alpha < 1/2. We investigate how small the error term in the asymptotic formula for the integer-counting function N(x) can be for such systems. In particular, we show that N(x) -...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Hauptverfasser: Broucke, Frederik, Hilberdink, Titus
Format: Artikel
Sprache:eng
Schlagworte:
Beurling generalized prime number systems
Mathematics and Statistics
omega-results for generalized integers
well-behaved number systems
Online-Zugang:Volltext bestellen
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue
container_start_page
container_title
container_volume
creator Broucke, Frederik
Hilberdink, Titus
description We consider Beurling number systems with very well-behaved primes, in the sense that psi(x) = x + O(x(alpha)) for some alpha < 1/2. We investigate how small the error term in the asymptotic formula for the integer-counting function N(x) can be for such systems. In particular, we show that N(x) - rho x = ohm(root x e-(log x)beta ) for any beta > 2/3.
format Article
fullrecord <record><control><sourceid>ghent_ADGLB</sourceid><recordid>TN_cdi_ghent_librecat_oai_archive_ugent_be_01J06A1RC0DQ0XX1TXPCF13HZW</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>oai_archive_ugent_be_01J06A1RC0DQ0XX1TXPCF13HZW</sourcerecordid><originalsourceid>FETCH-ghent_librecat_oai_archive_ugent_be_01J06A1RC0DQ0XX1TXPCF13HZW3</originalsourceid><addsrcrecordid>eNqtzMEKgjAYwPEdCpLyHfYCwj4tq6OZIp0qhKTLmPY5B2vCNjv09BH0CJ3-hx_8ZySAbcKiNE7XCxI6p1oWww5gw_YBgczQ8YlSRBbdpD3tR0sPOFmtjKQSDVqh1RsfVBmPEq1bkXkvtMPw1yUpyqLOq0gOaDzXqrXYCc9Hobiw3aBeyCf5pRY5gxNLM7jm7HhhTQN1c85LSKr7LfnX5wNXekt0</addsrcrecordid><sourcetype>Institutional Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>An omega-result for Beurling generalized integers</title><source>Ghent University Academic Bibliography</source><creator>Broucke, Frederik ; Hilberdink, Titus</creator><creatorcontrib>Broucke, Frederik ; Hilberdink, Titus</creatorcontrib><description>We consider Beurling number systems with very well-behaved primes, in the sense that psi(x) = x + O(x(alpha)) for some alpha &lt; 1/2. We investigate how small the error term in the asymptotic formula for the integer-counting function N(x) can be for such systems. In particular, we show that N(x) - rho x = ohm(root x e-(log x)beta ) for any beta &gt; 2/3.</description><identifier>ISSN: 1730-6264</identifier><identifier>ISSN: 0065-1036</identifier><language>eng</language><subject>Beurling generalized prime number systems ; Mathematics and Statistics ; omega-results for generalized integers ; well-behaved number systems</subject><creationdate>2024</creationdate><rights>No license (in copyright) info:eu-repo/semantics/openAccess</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>315,776,27837</link.rule.ids><linktorsrc>$$Uhttp://hdl.handle.net/1854/LU-01J06A1RC0DQ0XX1TXPCF13HZW$$EView_record_in_Ghent_University$$FView_record_in_$$GGhent_University$$Hfree_for_read</linktorsrc></links><search><creatorcontrib>Broucke, Frederik</creatorcontrib><creatorcontrib>Hilberdink, Titus</creatorcontrib><title>An omega-result for Beurling generalized integers</title><description>We consider Beurling number systems with very well-behaved primes, in the sense that psi(x) = x + O(x(alpha)) for some alpha &lt; 1/2. We investigate how small the error term in the asymptotic formula for the integer-counting function N(x) can be for such systems. In particular, we show that N(x) - rho x = ohm(root x e-(log x)beta ) for any beta &gt; 2/3.</description><subject>Beurling generalized prime number systems</subject><subject>Mathematics and Statistics</subject><subject>omega-results for generalized integers</subject><subject>well-behaved number systems</subject><issn>1730-6264</issn><issn>0065-1036</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>ADGLB</sourceid><recordid>eNqtzMEKgjAYwPEdCpLyHfYCwj4tq6OZIp0qhKTLmPY5B2vCNjv09BH0CJ3-hx_8ZySAbcKiNE7XCxI6p1oWww5gw_YBgczQ8YlSRBbdpD3tR0sPOFmtjKQSDVqh1RsfVBmPEq1bkXkvtMPw1yUpyqLOq0gOaDzXqrXYCc9Hobiw3aBeyCf5pRY5gxNLM7jm7HhhTQN1c85LSKr7LfnX5wNXekt0</recordid><startdate>2024</startdate><enddate>2024</enddate><creator>Broucke, Frederik</creator><creator>Hilberdink, Titus</creator><scope>ADGLB</scope></search><sort><creationdate>2024</creationdate><title>An omega-result for Beurling generalized integers</title><author>Broucke, Frederik ; Hilberdink, Titus</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-ghent_librecat_oai_archive_ugent_be_01J06A1RC0DQ0XX1TXPCF13HZW3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Beurling generalized prime number systems</topic><topic>Mathematics and Statistics</topic><topic>omega-results for generalized integers</topic><topic>well-behaved number systems</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Broucke, Frederik</creatorcontrib><creatorcontrib>Hilberdink, Titus</creatorcontrib><collection>Ghent University Academic Bibliography</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Broucke, Frederik</au><au>Hilberdink, Titus</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>An omega-result for Beurling generalized integers</atitle><date>2024</date><risdate>2024</risdate><issn>1730-6264</issn><issn>0065-1036</issn><abstract>We consider Beurling number systems with very well-behaved primes, in the sense that psi(x) = x + O(x(alpha)) for some alpha &lt; 1/2. We investigate how small the error term in the asymptotic formula for the integer-counting function N(x) can be for such systems. In particular, we show that N(x) - rho x = ohm(root x e-(log x)beta ) for any beta &gt; 2/3.</abstract><oa>free_for_read</oa></addata></record>
fulltext fulltext_linktorsrc
identifier ISSN: 1730-6264
ispartof
issn 1730-6264
0065-1036
language eng
recordid cdi_ghent_librecat_oai_archive_ugent_be_01J06A1RC0DQ0XX1TXPCF13HZW
source Ghent University Academic Bibliography
subjects Beurling generalized prime number systems
Mathematics and Statistics
omega-results for generalized integers
well-behaved number systems
title An omega-result for Beurling generalized integers
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-04T17%3A07%3A29IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-ghent_ADGLB&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=An%20omega-result%20for%20Beurling%20generalized%20integers&rft.au=Broucke,%20Frederik&rft.date=2024&rft.issn=1730-6264&rft_id=info:doi/&rft_dat=%3Cghent_ADGLB%3Eoai_archive_ugent_be_01J06A1RC0DQ0XX1TXPCF13HZW%3C/ghent_ADGLB%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true