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Online Theses in Number Theory

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Dissertations / Theses on the topic 'Number theory'

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Buchanan, Dan Matthews. "Analytic Number Theory and the Prime Number Theorem." Youngstown State University / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1525451327211365.

Maynard, James. "Topics in analytic number theory." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:3bf4346a-3efe-422a-b9b7-543acd529269.

Guo, Charng Rang. "On analytic number theory." Thesis, University of Oxford, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.357394.

Harbour, Daniel 1975. "Elements of number theory." Thesis, Massachusetts Institute of Technology, 2003. http://hdl.handle.net/1721.1/17581.

Anderson, Crystal Lynn. "An Introduction to Number Theory Prime Numbers and Their Applications." Digital Commons @ East Tennessee State University, 2006. https://dc.etsu.edu/etd/2222.

Alkauskas, Giedrius. "Several problems from number theory." Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2009. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2009~D_20091008_155751-23469.

Dyke, Steven Douglas. "Topics in analytic number theory." Thesis, University of Oxford, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.334817.

Amirkhanyan, Gagik M. "Problems in combinatorial number theory." Diss., Georgia Institute of Technology, 2014. http://hdl.handle.net/1853/51865.

Rowe, Paul Michael Dominic. "Contributions to metric number theory." Thesis, Royal Holloway, University of London, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.408263.

Irving, Alastair James. "Topics in analytic number theory." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:40f5511c-af6b-4215-b1ab-97f203e8936b.

Letendre, Patrick. "Topics in analytic number theory." Doctoral thesis, Université Laval, 2018. http://hdl.handle.net/20.500.11794/31443.

Powell, Kevin James. "Topics in Analytic Number Theory." BYU ScholarsArchive, 2009. https://scholarsarchive.byu.edu/etd/2084.

Bulinski, Kamil. "Interactions between Ergodic Theory and Combinatorial Number Theory." Thesis, The University of Sydney, 2017. http://hdl.handle.net/2123/17733.

Ho, Kwan-hung, and 何君雄. "On the prime twins conjecture and almost-prime k-tuples." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2002. http://hub.hku.hk/bib/B29768421.

Chan, Ching-yin, and 陳靖然. "On k-tuples of almost primes." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2013. http://hdl.handle.net/10722/195967.

Bronder, Justin S. "The AKS Class of Primality Tests: A Proof of Correctness and Parallel Implementation." Fogler Library, University of Maine, 2006. http://www.library.umaine.edu/theses/pdf/BronderJS2006.pdf.

Röttger, Christian Gottfried Johannes. "Counting problems in algebraic number theory." Thesis, University of East Anglia, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.327407.

Watt, N. "some problems in analytic number theory." Thesis, Bucks New University, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.384667.

Baker, Liam Bradwin. "Analytic methods in combinatorial number theory." Thesis, Stellenbosch : Stellenbosch University, 2015. http://hdl.handle.net/10019.1/98017.

Örström, Simon. "Diophantine approximation and metric number theory." Thesis, Uppsala universitet, Analys och sannolikhetsteori, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-452458.

Hoffman, John W. "Some Problems in Additive Number Theory." Kent State University / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=kent1408298984.

Acciaro, Vincenzo Carleton University Dissertation Computer Science. "Local global methods in number theory." Ottawa, 1995.

Shoup, Victor. "Removing randomness from computational number theory." Madison, Wis. : University of Wisconsin-Madison, Computer Sciences Dept, 1989. http://catalog.hathitrust.org/api/volumes/oclc/20839526.html.

Loveless, Andrew David. "Extensions in the theory of Lucas and Lehmer pseudoprimes." Online access for everyone, 2005. http://www.dissertations.wsu.edu/Dissertations/Summer2005/a%5Floveless%5F070705.pdf.

Shahabi, Majid. "The distribution of the classical error terms of prime number theory." Thesis, Lethbridge, Alta. : University of Lethbridge, Dept. of Mathematics and Computer Science, c2012, 2012. http://hdl.handle.net/10133/3252.

Burns, Jonathan. "Recursive Methods in Number Theory, Combinatorial Graph Theory, and Probability." Scholar Commons, 2014. https://scholarcommons.usf.edu/etd/5193.

at, Gerald Teschl@univie ac. "On the Number of Eigenvalues of Jacobi Operators." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi1079.ps.

Schinck, Amelie. "The local-global principle in number theory." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/MQ64047.pdf.

Dyer, A. K. "Applications of sieve methods in number theory." Thesis, Bucks New University, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.384646.

Walker, Aled. "Topics in analytic and combinatorial number theory." Thesis, University of Oxford, 2018. http://ora.ox.ac.uk/objects/uuid:0d48a697-fd7a-4aca-bebe-4806322bdbbd.

Brewer, Sky J. "Results in metric and analytic number theory." Thesis, University of York, 2017. http://etheses.whiterose.ac.uk/18381/.

Griffin, Cornelius John. "Subgroups of infinite groups : interactions between group theory and number theory." Thesis, University of Nottingham, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.252018.

Ki, Haseo Kechris A. S. Kechris A. S. "Topics in descriptive set theory related to number theory and analysis /." Diss., Pasadena, Calif. : California Institute of Technology, 1995. http://resolver.caltech.edu/CaltechETD:etd-10112007-111738.

Hughes, Garry. "Distribution of additive functions in algebraic number fields." Title page, contents and summary only, 1987. http://web4.library.adelaide.edu.au/theses/09SM/09smh893.pdf.

Kong, Yafang, and 孔亚方. "On linear equations in primes and powers of two." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2013. http://hub.hku.hk/bib/B50533769.

Ketkar, Pallavi S. (Pallavi Subhash). "Primitive Substitutive Numbers are Closed under Rational Multiplication." Thesis, University of North Texas, 1998. https://digital.library.unt.edu/ark:/67531/metadc278637/.

Trad, Mohamad. "The proof of Fermat's last theorem." CSUSB ScholarWorks, 2000. https://scholarworks.lib.csusb.edu/etd-project/1690.

Harper, Adam James. "Some topics in analytic and probabilistic number theory." Thesis, University of Cambridge, 2012. https://www.repository.cam.ac.uk/handle/1810/265539.

Tringali, Salvatore. "Some questions in combinatorial and elementary number theory." Phd thesis, Université Jean Monnet - Saint-Etienne, 2013. http://tel.archives-ouvertes.fr/tel-01060871.

Thorn, Rebecca Emily. "Metric number theory : the good and the bad." Thesis, Queen Mary, University of London, 2005. http://qmro.qmul.ac.uk/xmlui/handle/123456789/28568.

Matomaki, Kaisa Sofia. "Applications of sieve methods in analytic number theory." Thesis, University of London, 2009. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.549585.

Olofsson, Rikard. "Problems in Number Theory related to Mathematical Physics." Doctoral thesis, Stockholm : Engineering sciences, Kungliga Tekniska högskolan, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-9514.

Swanson, Colleen M. "Algebraic number fields and codes /." Connect to online version, 2006. http://ada.mtholyoke.edu/setr/websrc/pdfs/www/2006/172.pdf.

Polzin, Marc. "Prolongement de la valeur absolue de Gauss et problème de Skolem." Bordeaux 1, 1987. http://www.theses.fr/1987BOR10539.

Landreau, Bernard. "Majorations de fonctions arithmétiques en moyenne sur des ensembles de faible densité." Bordeaux 1, 1987. http://www.theses.fr/1987BOR10629.

Louboutin, Stéphane. "Arithmetique des corps quadratiques reels et fractions continues." Paris 7, 1987. http://www.theses.fr/1987PA077077.

Emsalem, Michel. "I : Deux problèmes d'analyse réelle et p-adique. II: Autour de la conjecture de Leopoldt : Un point de vue transcendant." Paris 6, 1987. http://www.theses.fr/1987PA066069.

Langevin, Michel. "Methodes transcendantes en theorie des nombres." Paris 6, 1987. http://www.theses.fr/1987PA066178.

Balazard, Michel. "Sur la repartition des valeurs de certaines fonctions arithmetiques additives." Limoges, 1987. http://www.theses.fr/1987LIMO0014.

Azzouza, Nour-Eddine. "Majorations effectives du nombre d'entiers inferieurs a x, et ayant exactement k facteurs premiers." Limoges, 1988. http://www.theses.fr/1988LIMO0032.

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• Prime Number Theorem
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Topics in Number Theory

• © 1988
• J. S. Chahal 0

Brigham Young University, Provo, USA

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Table of contents (8 chapters)

Front matter, basic properties of the integers.

J. S. Chahal

Algebraic Methods

Representation of integers by forms, algebraic number fields, algebraic curves, the mordell-weil theorem, computation of the mordell-weil group, equations over finite fields, back matter.

• finite field
• mathematics
• number theory

About this book

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Book Title : Topics in Number Theory

Authors : J. S. Chahal

Series Title : University Series in Mathematics

DOI : https://doi.org/10.1007/978-1-4899-0439-3

Publisher : Springer New York, NY

eBook Packages : Springer Book Archive

Copyright Information : Springer Science+Business Media New York 1988

Hardcover ISBN : 978-0-306-42866-1 Published: 30 June 1988

Softcover ISBN : 978-1-4899-0441-6 Published: 05 June 2013

eBook ISBN : 978-1-4899-0439-3 Published: 11 November 2013

Edition Number : 1

Number of Pages : XIV, 191

Topics : Algebra

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• Dr. Andrew Sutherland

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• Mathematics

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• Algebra and Number Theory
• Topology and Geometry

Learning Resource Types

Number theory i, lecture notes.

The complete lecture notes Number Theory I (PDF - 2.7 MB) can be used as the online textbook for this course.

Lecture 1: Absolute Values and Discrete Valuations (PDF)

Lecture 2: Localization and Dedekind Domains (PDF)

Lecture 3: Properties of Dedekind Domains and Factorization of Ideals (PDF)

Lecture 4: Étale Algebras, Norm and Trace (PDF)

Lecture 5: Dedekind Extensions (PDF)

Lecture 6: Ideal Norms and the Dedekind-Kummer Theorem (PDF)

Lecture 7: Galois Extensions, Frobenius Elements, and the Artin Map (PDF)

Lecture 8: Complete Fields and Valuation Rings (PDF)

Lecture 9: Local Fields and Hensel’s Lemmas (PDF)

Lecture 10: Extensions of Complete DVRs (PDF)

Lecture 11: Totally Ramified Extensions and Krasner’s Lemma (PDF)

Lecture 12: The Different and the Discriminant (PDF)

Lecture 13: Global Fields and the Product Formula (PDF)

Lecture 14: The Geometry of Numbers (PDF)

Lecture 15: Dirichlet’s Unit Theorem (PDF)

Lecture 16: Riemann’s Zeta Function and the Prime Number Theorem (PDF)

Lecture 17: The Functional Equation (PDF)

Lecture 18: Dirichlet L-functions and Primes in Arithmetic Progressions (PDF)

Lecture 19: The Analytic Class Number Formula (PDF)

Lecture 20: The Kronecker-Weber Theorem (PDF)

Lecture 21: Class Field Theory: Ray Class Groups and Ray Class Fields (PDF)

Lecture 22: The Main Theorems of Global Class Field Theory (PDF)

Lecture 23: Tate Cohomology (PDF)

Lecture 24: Artin Reciprocity in the Unramified Case (PDF)

Lecture 25: The Ring of Adeles and Strong Approximation (PDF)

Lecture 26: The Idele Group, Profinite Groups, and Infinite Galois Theory (PDF)

Lecture 27: Local Class Field Theory (PDF)

Lecture 28: Global Class Field Theory and the Chebotarev Density Theorem (PDF)

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Number theory studies some of the most basic objects of mathematics: integers and prime numbers. It is a huge subject that makes contact with most areas of modern mathematics, and in fact, enjoys a symbiotic relationship with many. The last fifty years in particular have seen some dramatic progress, including Deligne's proof of the Weil conjectures (giving optimal asymptotics for the number of solutions of polynomial equations over finite fields), Faltings' proof of the Mordell conjecture (establishing finiteness of rational points on hyperbolic curves), Wiles' proof of Fermat's last theorem (which brought a 400-year-long quest to completion) and Zhang's proof of the boundedness of prime gaps (taking a huge step towards the twin prime conjecture). The solutions to these problems rely on techniques from many areas, including algebraic and complex geometry, representation theory and modular forms, differential and algebraic topology, and real and complex analysis. Moreover, grand new vistas (such as the Langlands program) have been uncovered, which will surely keep mathematicians busy for decades.

The research interests of our group are diverse and reflect the breadth of the subject. They include arithmetic as well as classical algebraic geometry; automorphic, geometric and p-adic representation theory; Shimura varieties and Galois representations; p-adic Hodge theory; harmonic analysis and analytic number theory; representation stability and commutative algebra; and algorithmic and computational number theory.

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