Distinctness of the Lifted Kloosterman Sums over the Prime Field Fp

Distinctness of the Lifted Kloosterman Sums over the Prime Field Fp | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Distinctness of the Lifted Kloosterman Sums over the Prime Field Fp Lyubomir Borissov This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3823912/v2 This work is licensed under a CC BY 4.0 License Status: Posted Version 2 posted You are reading this latest preprint version Show more versions Abstract In this paper we show that Kloosterman sums Kpm(u); u ∈ F*p; are distinct for arbitrary odd characteristic p and each degree of extension m of the prime field Fp. Pure Mathematics Kloosterman sums finite fields trace Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 2 posted You are reading this latest preprint version Show more versions Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3823912","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":264901963,"identity":"fceec80a-08db-4220-a1de-c88b5b451a20","order_by":0,"name":"Lyubomir Borissov","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA5ElEQVRIiWNgGAWjYBACPgYeBmYGBhsefiAHyDgApHjwa2GDaEmTk2xgYGwmRcthY4MDRGuRyD34uODP4cTN1w4/f1zAcEdevoH38Av8WvKSjWe2pSduu51m2DyD4ZnhhgN8aRb4teSYSfM2WAO1JBg28zAcZtzAwGNmQFALzx/mxM2z0z+CtNjPbyBKC5uzsYF0DtiWxIYDPMYP8GrheQfyS5qcxO2cwtk8Bs+SNxzmS8Ong4GfHRxiwKicnb7hM0/FHdv57b2HP+DVgwpAnmAGupYELRDATIoto2AUjIJRMPwBAJy2SBRBTgZFAAAAAElFTkSuQmCC","orcid":"","institution":"IMI, BAS","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Lyubomir","middleName":"","lastName":"Borissov","suffix":""}],"badges":[],"createdAt":"2023-12-30 11:58:59","currentVersionCode":2,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false,"coiExplicitlySet":false},"doi":"10.21203/rs.3.rs-3823912/v2","doiUrl":"https://doi.org/10.21203/rs.3.rs-3823912/v2","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":50322123,"identity":"b349147c-0cd0-4eed-8768-6d044ac46ad5","added_by":"auto","created_at":"2024-01-29 17:45:13","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":206469,"visible":true,"origin":"","legend":"","description":"","filename":"klosterdistliftlyb.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3823912/v2_covered_e7e6c61f-c766-4220-a126-e0d97811bbf2.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eDistinctness of the Lifted Kloosterman Sums over the Prime Field Fp\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Institute of Mathematics and informatics , Bulgarian Academy of Sciences","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Kloosterman sums, finite fields, trace","lastPublishedDoi":"10.21203/rs.3.rs-3823912/v2","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3823912/v2","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this paper we show that Kloosterman sums Kpm(u); 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