Persistent Link:
http://hdl.handle.net/10150/290585
Title:
On zeros of characteristic p zeta functions
Author:
Diaz-Vargas, Javier Arturo, 1952-
Issue Date:
1996
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
The location and multiplicity of the zeros of zeta functions encode interesting arithmetic information. We study characteristic p zeta functions of Carlitz and Goss. We present a simpler proof of the fact that "non-trivial" zeros of a characteristic p zeta function satisfy Goss' analogue of the Riemann Hypothesis for F(q)[T]. We also prove simplicity of these zeros, and give partial results for F(q)[T] where q is not necessarily prime. Then we focus on "trivial" zeros, but for characteristic p zeta functions for general function fields over finite fields. Here, we prove a theorem on zeros at negative integers for characteristic p zeta functions, showing more vanishing than that suggested by naive analogies. We also compute some concrete examples providing the extra vanishing, when the class number is more than one. Finally, we give an application of these results related to the non-vanishing of certain class group components for cyclotomic function fields. In particular, we give examples of function fields, where all the primes of degree more than two are "irregular", in the sense of the Drinfeld-Hayes cyclotomic theory.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Mathematics.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Mathematics
Degree Grantor:
University of Arizona
Advisor:
Thakur, Dinesh S.

Full metadata record

DC FieldValue Language
dc.language.isoen_USen_US
dc.titleOn zeros of characteristic p zeta functionsen_US
dc.creatorDiaz-Vargas, Javier Arturo, 1952-en_US
dc.contributor.authorDiaz-Vargas, Javier Arturo, 1952-en_US
dc.date.issued1996en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractThe location and multiplicity of the zeros of zeta functions encode interesting arithmetic information. We study characteristic p zeta functions of Carlitz and Goss. We present a simpler proof of the fact that "non-trivial" zeros of a characteristic p zeta function satisfy Goss' analogue of the Riemann Hypothesis for F(q)[T]. We also prove simplicity of these zeros, and give partial results for F(q)[T] where q is not necessarily prime. Then we focus on "trivial" zeros, but for characteristic p zeta functions for general function fields over finite fields. Here, we prove a theorem on zeros at negative integers for characteristic p zeta functions, showing more vanishing than that suggested by naive analogies. We also compute some concrete examples providing the extra vanishing, when the class number is more than one. Finally, we give an application of these results related to the non-vanishing of certain class group components for cyclotomic function fields. In particular, we give examples of function fields, where all the primes of degree more than two are "irregular", in the sense of the Drinfeld-Hayes cyclotomic theory.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectMathematics.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorThakur, Dinesh S.en_US
dc.identifier.proquest9706172en_US
dc.identifier.bibrecord.b34294065en_US
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