A reciprocity law in function fields

We generalize Gauss’ lemma over function fields, and establish a reciprocity law for power residue symbols. As an application, a reciprocity law for power residue symbols is established in totally imaginary function fields.

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Archiv der Mathematik 2024, Vol.123 (1), p.49-56
1. Verfasser:	Hamahata, Yoshinori
Format:	Artikel
Sprache:	eng
Schlagworte:	Mathematics Mathematics and Statistics Reciprocity Residues Symbols
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

container_end_page	56
container_issue	1
container_start_page	49
container_title	Archiv der Mathematik
container_volume	123
creator	Hamahata, Yoshinori
description	We generalize Gauss’ lemma over function fields, and establish a reciprocity law for power residue symbols. As an application, a reciprocity law for power residue symbols is established in totally imaginary function fields.
doi_str_mv	10.1007/s00013-024-02006-9
format	Article
fullrecord	<record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_3071257200</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>3071257200</sourcerecordid><originalsourceid>FETCH-LOGICAL-c270t-5438457c27fb78d9d3a57b3feecde4215918aa9dd3b78fe2856cb920ae7ffb5a3</originalsourceid><addsrcrecordid>eNp9UMFKxDAQDaJgXf0BTwW9RidJs0mOy6KrsOBFwVtI00S61HZNWmT_3tEK3jwMM8O892bmEXLJ4IYBqNsMAExQ4BUGwJKaI1KwigPVRuhjUuBcUK3N6yk5y3mHaK6VKcj1qkzBt_s0-HY8lJ37LNu-jFPvx3bAog1dk8_JSXRdDhe_eUFe7u-e1w90-7R5XK-21HMFI5WV0JVU2MRa6cY0wklVixiCb0LFmTRMO2eaRuA4Bq7l0teGgwsqxlo6sSBXsy6e8zGFPNrdMKUeV1oBinGp8DdE8Rnl05BzCtHuU_vu0sEysN9u2NkNi27YHzesQZKYSRnB_VtIf9L_sL4AjixhCg</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>3071257200</pqid></control><display><type>article</type><title>A reciprocity law in function fields</title><source>Springer Nature - Complete Springer Journals</source><creator>Hamahata, Yoshinori</creator><creatorcontrib>Hamahata, Yoshinori</creatorcontrib><description>We generalize Gauss’ lemma over function fields, and establish a reciprocity law for power residue symbols. As an application, a reciprocity law for power residue symbols is established in totally imaginary function fields.</description><identifier>ISSN: 0003-889X</identifier><identifier>EISSN: 1420-8938</identifier><identifier>DOI: 10.1007/s00013-024-02006-9</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Mathematics ; Mathematics and Statistics ; Reciprocity ; Residues ; Symbols</subject><ispartof>Archiv der Mathematik, 2024, Vol.123 (1), p.49-56</ispartof><rights>The Author(s) 2024</rights><rights>Copyright Springer Nature B.V. 2024</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c270t-5438457c27fb78d9d3a57b3feecde4215918aa9dd3b78fe2856cb920ae7ffb5a3</cites><orcidid>0000-0003-1849-0725</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00013-024-02006-9$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00013-024-02006-9$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,777,781,27905,27906,41469,42538,51300</link.rule.ids></links><search><creatorcontrib>Hamahata, Yoshinori</creatorcontrib><title>A reciprocity law in function fields</title><title>Archiv der Mathematik</title><addtitle>Arch. Math</addtitle><description>We generalize Gauss’ lemma over function fields, and establish a reciprocity law for power residue symbols. As an application, a reciprocity law for power residue symbols is established in totally imaginary function fields.</description><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Reciprocity</subject><subject>Residues</subject><subject>Symbols</subject><issn>0003-889X</issn><issn>1420-8938</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><recordid>eNp9UMFKxDAQDaJgXf0BTwW9RidJs0mOy6KrsOBFwVtI00S61HZNWmT_3tEK3jwMM8O892bmEXLJ4IYBqNsMAExQ4BUGwJKaI1KwigPVRuhjUuBcUK3N6yk5y3mHaK6VKcj1qkzBt_s0-HY8lJ37LNu-jFPvx3bAog1dk8_JSXRdDhe_eUFe7u-e1w90-7R5XK-21HMFI5WV0JVU2MRa6cY0wklVixiCb0LFmTRMO2eaRuA4Bq7l0teGgwsqxlo6sSBXsy6e8zGFPNrdMKUeV1oBinGp8DdE8Rnl05BzCtHuU_vu0sEysN9u2NkNi27YHzesQZKYSRnB_VtIf9L_sL4AjixhCg</recordid><startdate>2024</startdate><enddate>2024</enddate><creator>Hamahata, Yoshinori</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0003-1849-0725</orcidid></search><sort><creationdate>2024</creationdate><title>A reciprocity law in function fields</title><author>Hamahata, Yoshinori</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-5438457c27fb78d9d3a57b3feecde4215918aa9dd3b78fe2856cb920ae7ffb5a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Reciprocity</topic><topic>Residues</topic><topic>Symbols</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Hamahata, Yoshinori</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>CrossRef</collection><jtitle>Archiv der Mathematik</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Hamahata, Yoshinori</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A reciprocity law in function fields</atitle><jtitle>Archiv der Mathematik</jtitle><stitle>Arch. Math</stitle><date>2024</date><risdate>2024</risdate><volume>123</volume><issue>1</issue><spage>49</spage><epage>56</epage><pages>49-56</pages><issn>0003-889X</issn><eissn>1420-8938</eissn><abstract>We generalize Gauss’ lemma over function fields, and establish a reciprocity law for power residue symbols. As an application, a reciprocity law for power residue symbols is established in totally imaginary function fields.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00013-024-02006-9</doi><tpages>8</tpages><orcidid>https://orcid.org/0000-0003-1849-0725</orcidid><oa>free_for_read</oa></addata></record>
fulltext	fulltext
identifier	ISSN: 0003-889X
ispartof	Archiv der Mathematik, 2024, Vol.123 (1), p.49-56
issn	0003-889X 1420-8938
language	eng
recordid	cdi_proquest_journals_3071257200
source	Springer Nature - Complete Springer Journals
subjects	Mathematics Mathematics and Statistics Reciprocity Residues Symbols
title	A reciprocity law in function fields
url	https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-19T20%3A58%3A51IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=A%20reciprocity%20law%20in%20function%20fields&rft.jtitle=Archiv%20der%20Mathematik&rft.au=Hamahata,%20Yoshinori&rft.date=2024&rft.volume=123&rft.issue=1&rft.spage=49&rft.epage=56&rft.pages=49-56&rft.issn=0003-889X&rft.eissn=1420-8938&rft_id=info:doi/10.1007/s00013-024-02006-9&rft_dat=%3Cproquest_cross%3E3071257200%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=3071257200&rft_id=info:pmid/&rfr_iscdi=true