{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/78348"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/78348","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Extensions of Selberg-Delange method","abstract":"This dissertation involves two topics in analytic number theory. The first topic focuses on extensions of the Selberg-Delange Method, which are discussed in Chapters $2$ and $3$. The last topic, which is discussed in Chapter $4$, is a new identity for Multiple Zeta Values. The Selberg-Delange method is a method that is widely used to determine the asymptotic behavior of the sum of arithmetic functions whose corresponding Dirichlet's series can be written in the term of the Riemann zeta function, $\\zeta(s)$. In Chapter $2$, we first provide a history and recent developments of the Selberg-Delange method. Then, we provide a generalized version of the Selberg-Delange method which can be applied to a larger class of arithmetic functions. We devote Chapter $3$ to the proofs of the results stated in Chapter $2$. In $1961$, Matsuoka evaluated $\\zeta(2)$ by means of evaluating the integral $\\ds \\int_0^{\\pi/2} x^{2}\\cos^{2n}(x) dx$. The last chapter of this dissertation generalizes the idea of Matsuoka and obtains a new identity for Multiple Zeta Values.","abstract_html":"This dissertation involves two topics in analytic number theory. The first topic focuses on extensions of the Selberg-Delange Method, which are discussed in Chapters $2$ and $3$. The last topic, which is discussed in Chapter $4$, is a new identity for Multiple Zeta Values. The Selberg-Delange method is a method that is widely used to determine the asymptotic behavior of the sum of arithmetic functions whose corresponding Dirichlet's series can be written in the term of the Riemann zeta function, $\\zeta(s)$. In Chapter $2$, we first provide a history and recent developments of the Selberg-Delange method. Then, we provide a generalized version of the Selberg-Delange method which can be applied to a larger class of arithmetic functions. We devote Chapter $3$ to the proofs of the results stated in Chapter $2$. In $1961$, Matsuoka evaluated $\\zeta(2)$ by means of evaluating the integral \\ds \\int0π/2 x2\\cos2n(x) dx. The last chapter of this dissertation generalizes the idea of Matsuoka and obtains a new identity for Multiple Zeta Values.","abstract_has_math":true,"creators":["Phaovibul, Mtip Easter"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Berndt, Bruce C.","Zaharescu, Alexandru","Ford, Kevin B","Hildebrand, Adolf J"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-07-22T22:16:28Z","date_published":"2015-07-22T22:16:28Z","updated_at":"2026-07-22T22:26:11Z","subjects":["Multiple Zeta function","Selberg-Delange Method","Asymptotic","Riemann Zeta function"],"languages":["en"],"rights":["Copyright 2015 Mtip Phaovibul"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/78348","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Berndt, Bruce C.","Zaharescu, Alexandru","Ford, Kevin B","Hildebrand, Adolf J"]},{"key":"dc:creator","label":"Author","values":["Phaovibul, Mtip Easter"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-07-22T22:16:28Z","2015-05","2015-04-03","2015-5"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Multiple Zeta function","Selberg-Delange Method","Asymptotic","Riemann Zeta function"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2015 Mtip Phaovibul"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/78348"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["This dissertation involves two topics in analytic number theory. The first topic focuses on extensions of the Selberg-Delange Method, which are discussed in Chapters $2$ and $3$. The last topic, which is discussed in Chapter $4$, is a new identity for Multiple Zeta Values. The Selberg-Delange method is a method that is widely used to determine the asymptotic behavior of the sum of arithmetic functions whose corresponding Dirichlet's series can be written in the term of the Riemann zeta function, $\\zeta(s)$. In Chapter $2$, we first provide a history and recent developments of the Selberg-Delange method. Then, we provide a generalized version of the Selberg-Delange method which can be applied to a larger class of arithmetic functions. We devote Chapter $3$ to the proofs of the results stated in Chapter $2$. In $1961$, Matsuoka evaluated $\\zeta(2)$ by means of evaluating the integral $\\ds \\int_0^{\\pi/2} x^{2}\\cos^{2n}(x) dx$. The last chapter of this dissertation generalizes the idea of Matsuoka and obtains a new identity for Multiple Zeta Values.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2015-07-22 without embargo terms","The student, Mtip Phaovibul, accepted the attached license on 2015-04-03 at 08:25.","The student, Mtip Phaovibul, submitted this Dissertation for approval on 2015-04-03 at 08:34.","This Dissertation was approved for publication on 2015-04-03 at 15:13.","DSpace SAF Submission Ingestion Package generated from Vireo submission #7786 on 2015-07-22 at 10:31:25","Made available in DSpace on 2015-07-22T22:16:28Z (GMT). No. of bitstreams: 2 PHAOVIBUL-DISSERTATION-2015.pdf: 521835 bytes, checksum: f9e1c793ae3409ece55b398a6572842b (MD5) LICENSE.txt: 4211 bytes, checksum: 54cc51cbf9dc71b5f20f4b5b1722ac86 (MD5) Previous issue date: 2015-04-03"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Extensions of Selberg-Delange method"]}]}],"canonical_facts":{"dc:contributor":["Berndt, Bruce C.","Zaharescu, Alexandru","Ford, Kevin B","Hildebrand, Adolf J"],"dc:creator":["Phaovibul, Mtip Easter"],"dc:date":["2015-07-22T22:16:28Z","2015-05","2015-04-03","2015-5"],"dc:description":["This dissertation involves two topics in analytic number theory. The first topic focuses on extensions of the Selberg-Delange Method, which are discussed in Chapters $2$ and $3$. The last topic, which is discussed in Chapter $4$, is a new identity for Multiple Zeta Values. The Selberg-Delange method is a method that is widely used to determine the asymptotic behavior of the sum of arithmetic functions whose corresponding Dirichlet's series can be written in the term of the Riemann zeta function, $\\zeta(s)$. In Chapter $2$, we first provide a history and recent developments of the Selberg-Delange method. Then, we provide a generalized version of the Selberg-Delange method which can be applied to a larger class of arithmetic functions. We devote Chapter $3$ to the proofs of the results stated in Chapter $2$. In $1961$, Matsuoka evaluated $\\zeta(2)$ by means of evaluating the integral $\\ds \\int_0^{\\pi/2} x^{2}\\cos^{2n}(x) dx$. The last chapter of this dissertation generalizes the idea of Matsuoka and obtains a new identity for Multiple Zeta Values.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2015-07-22 without embargo terms","The student, Mtip Phaovibul, accepted the attached license on 2015-04-03 at 08:25.","The student, Mtip Phaovibul, submitted this Dissertation for approval on 2015-04-03 at 08:34.","This Dissertation was approved for publication on 2015-04-03 at 15:13.","DSpace SAF Submission Ingestion Package generated from Vireo submission #7786 on 2015-07-22 at 10:31:25","Made available in DSpace on 2015-07-22T22:16:28Z (GMT). No. of bitstreams: 2 PHAOVIBUL-DISSERTATION-2015.pdf: 521835 bytes, checksum: f9e1c793ae3409ece55b398a6572842b (MD5) LICENSE.txt: 4211 bytes, checksum: 54cc51cbf9dc71b5f20f4b5b1722ac86 (MD5) Previous issue date: 2015-04-03"],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/78348"],"dc:language":["en"],"dc:rights":["Copyright 2015 Mtip Phaovibul"],"dc:subject":["Multiple Zeta function","Selberg-Delange Method","Asymptotic","Riemann Zeta function"],"dc:title":["Extensions of Selberg-Delange method"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:11Z"}