Funciones Zeta locales de Igusa y polinomios de Bernstein
ilustraciones
- Autores:
-
Cifuentes Espitia, Luis Alejandro
- Tipo de recurso:
- Fecha de publicación:
- 2022
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/82506
- Palabra clave:
- 510 - Matemáticas::512 - Álgebra
Polinomios
Algebra de funciones
Polynomials
Function algebras
Zeta functions
Conjeture of polynomials
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
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| dc.title.spa.fl_str_mv |
Funciones Zeta locales de Igusa y polinomios de Bernstein |
| dc.title.translated.eng.fl_str_mv |
Local Igusa Zeta Functions and Bernstein Polynomials |
| title |
Funciones Zeta locales de Igusa y polinomios de Bernstein |
| spellingShingle |
Funciones Zeta locales de Igusa y polinomios de Bernstein 510 - Matemáticas::512 - Álgebra Polinomios Algebra de funciones Polynomials Function algebras Zeta functions Conjeture of polynomials |
| title_short |
Funciones Zeta locales de Igusa y polinomios de Bernstein |
| title_full |
Funciones Zeta locales de Igusa y polinomios de Bernstein |
| title_fullStr |
Funciones Zeta locales de Igusa y polinomios de Bernstein |
| title_full_unstemmed |
Funciones Zeta locales de Igusa y polinomios de Bernstein |
| title_sort |
Funciones Zeta locales de Igusa y polinomios de Bernstein |
| dc.creator.fl_str_mv |
Cifuentes Espitia, Luis Alejandro |
| dc.contributor.advisor.none.fl_str_mv |
Rodriguez, John Jaime |
| dc.contributor.author.none.fl_str_mv |
Cifuentes Espitia, Luis Alejandro |
| dc.subject.ddc.spa.fl_str_mv |
510 - Matemáticas::512 - Álgebra |
| topic |
510 - Matemáticas::512 - Álgebra Polinomios Algebra de funciones Polynomials Function algebras Zeta functions Conjeture of polynomials |
| dc.subject.lemb.spa.fl_str_mv |
Polinomios Algebra de funciones |
| dc.subject.lemb.eng.fl_str_mv |
Polynomials Function algebras |
| dc.subject.proposal.eng.fl_str_mv |
Zeta functions Conjeture of polynomials |
| description |
ilustraciones |
| publishDate |
2022 |
| dc.date.accessioned.none.fl_str_mv |
2022-10-27T16:57:26Z |
| dc.date.available.none.fl_str_mv |
2022-10-27T16:57:26Z |
| dc.date.issued.none.fl_str_mv |
2022 |
| dc.type.spa.fl_str_mv |
Trabajo de grado - Maestría |
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info:eu-repo/semantics/masterThesis |
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info:eu-repo/semantics/acceptedVersion |
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Text |
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https://repositorio.unal.edu.co/handle/unal/82506 |
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Universidad Nacional de Colombia |
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Repositorio Institucional Universidad Nacional de Colombia |
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https://repositorio.unal.edu.co/ |
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https://repositorio.unal.edu.co/handle/unal/82506 https://repositorio.unal.edu.co/ |
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Universidad Nacional de Colombia Repositorio Institucional Universidad Nacional de Colombia |
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spa |
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spa |
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RedCol LaReferencia |
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Albeverio, S. ; Khrennikov, A. ; Shelkovich, V.: Theory of p-adic distributions: linear and nonlinear models. Cambridge University Press, 2010 ( 370) Albis, V. ; Zu ̃niga, W.: Una introducción elemental a la teoría de las funciones zeta locales de Igusa. En: Lecturas Matemáticas, 20 (1999), Nr. 1, p. 5–33 Borevich, I. ; Shafarevich, I.: Number theory. Academic press, 198 Bories, B.: Zeta functions, Bernstein-Sato polynomials, and the monodromy conjecture. (2013) Denef, J.: Report on Igusa’s local zeta function. En: S ́eminaire Bourbaki 1990 (1991), Nr. 741, p. 359–386 Field, R. ; Gargeya, V. ; Robinson, M. ; Schoenberg, F. ; Scott, R.: THE IGUSA LOCAL ZETA FUNCTION FOR xn+ ym. (1994) Galindo, W.A.Zu ̃niga: Igusa ́s local zeta functions of semicuasihomogeneous polynomials. World Scientific, 2001 (Trans.Amer.Math) Gelfand, I.: Generalized Functions: Properties and operations, by IM Gelfand and GE Shilov, translated by E. Saletan. Vol. 1. Academic Press, 1964 Igusa, J.: Complex powers and asymptotic expansions. (1974) Igusa, J.: B-functions and p-adic integrals. En: Algebraic Analysis. Elsevier, 1988, p. 231–241 Igusa, J.: An Introduction to the Theory of Local Zeta Functions. American Mathematical Society, 2007 (AMS/IP studies in advanced mathematics.) Igusa, J. ; Raghavan, S.: Lectures on forms of higher degree. Vol. 59. Springer Berlin- Heidelberg-New York, 1978 J, Denef. ; Hoornaert.K: Newton Polyhedra and Igusa’s Local Zeta Function. (2001) Le, Dung T.: Algebraic Approach To Differential Equations. World Scientific, 2010 (World Scientific) Loeser, F.: Fonctions D’Igusa p-adiques et Polynomes de Berstein. En: American Journal of Mathematics 110 (1988), Nr. 1, p. 1–21 Noro.M: An efficient modular algorithm for computing the global b-function. (2002) |
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Atribución-NoComercial 4.0 Internacional |
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v, 44 páginas |
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application/pdf |
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Universidad Nacional de Colombia |
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Bogotá - Ciencias - Maestría en Ciencias - Matemáticas |
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Facultad de Ciencias |
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Bogotá, Colombia |
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Universidad Nacional de Colombia - Sede Bogotá |
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Atribución-NoComercial 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Rodriguez, John Jaimef7aad44f4406c46151ba93653d0b1b0dCifuentes Espitia, Luis Alejandro9592df6438f81616c05e1f25c1d156672022-10-27T16:57:26Z2022-10-27T16:57:26Z2022https://repositorio.unal.edu.co/handle/unal/82506Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/ilustracionesEl propósito del presente documento en el que se desarrolla el trabajo final de maestra, es estudiar la conjetura planteada en 1988 por el matemático Jun-ichi Igusa en [10]; la cual asegura una relación entre los polos de la función zeta local de Igusa Z(s, f) y los ceros del polinomio de Bernstein-Sato bf. Además, se abordan conceptos básicos en el área de análisis p-ádico y se estudia el comportamiento de familias particulares de polinomios f ∈ Zp[x1, x2, ..., xn] en dicha conjetura. (Texto tomado de la fuente)The purpose of this document, in which the master thesis is presented, is to study the conjecture raised in 1988 by the mathematician Jun-ichi Igusa; which ensures a relationship between the poles of the Igusa local zeta function $Z(s,f)$ and the zeros of the Bernstein-Sato polynomial $b_f$.\\ Also, it addresses basic concepts in the area of $p$-adic analysis and aims to study the behavior of particular families of polynomials $f \in \mathbb Z_p[x_1,x_2 ,...,x_n]$, in said conjecture.MaestríaMaestría en ciencias matematicasNúmeros p-ádicosv, 44 páginasapplication/pdfspaUniversidad Nacional de ColombiaBogotá - Ciencias - Maestría en Ciencias - MatemáticasFacultad de CienciasBogotá, ColombiaUniversidad Nacional de Colombia - Sede Bogotá510 - Matemáticas::512 - ÁlgebraPolinomiosAlgebra de funcionesPolynomialsFunction algebrasZeta functionsConjeture of polynomialsFunciones Zeta locales de Igusa y polinomios de BernsteinLocal Igusa Zeta Functions and Bernstein PolynomialsTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMRedColLaReferenciaAlbeverio, S. ; Khrennikov, A. ; Shelkovich, V.: Theory of p-adic distributions: linear and nonlinear models. Cambridge University Press, 2010 ( 370)Albis, V. ; Zu ̃niga, W.: Una introducción elemental a la teoría de las funciones zeta locales de Igusa. En: Lecturas Matemáticas, 20 (1999), Nr. 1, p. 5–33Borevich, I. ; Shafarevich, I.: Number theory. Academic press, 198Bories, B.: Zeta functions, Bernstein-Sato polynomials, and the monodromy conjecture. (2013)Denef, J.: Report on Igusa’s local zeta function. En: S ́eminaire Bourbaki 1990 (1991), Nr. 741, p. 359–386Field, R. ; Gargeya, V. ; Robinson, M. ; Schoenberg, F. ; Scott, R.: THE IGUSA LOCAL ZETA FUNCTION FOR xn+ ym. (1994)Galindo, W.A.Zu ̃niga: Igusa ́s local zeta functions of semicuasihomogeneous polynomials. World Scientific, 2001 (Trans.Amer.Math)Gelfand, I.: Generalized Functions: Properties and operations, by IM Gelfand and GE Shilov, translated by E. Saletan. Vol. 1. Academic Press, 1964Igusa, J.: Complex powers and asymptotic expansions. (1974)Igusa, J.: B-functions and p-adic integrals. En: Algebraic Analysis. Elsevier, 1988, p. 231–241Igusa, J.: An Introduction to the Theory of Local Zeta Functions. American Mathematical Society, 2007 (AMS/IP studies in advanced mathematics.)Igusa, J. ; Raghavan, S.: Lectures on forms of higher degree. Vol. 59. Springer Berlin- Heidelberg-New York, 1978J, Denef. ; Hoornaert.K: Newton Polyhedra and Igusa’s Local Zeta Function. (2001)Le, Dung T.: Algebraic Approach To Differential Equations. World Scientific, 2010 (World Scientific)Loeser, F.: Fonctions D’Igusa p-adiques et Polynomes de Berstein. En: American Journal of Mathematics 110 (1988), Nr. 1, p. 1–21Noro.M: An efficient modular algorithm for computing the global b-function. (2002)Público generalLICENSElicense.txtlicense.txttext/plain; charset=utf-85879https://repositorio.unal.edu.co/bitstream/unal/82506/1/license.txteb34b1cf90b7e1103fc9dfd26be24b4aMD51ORIGINAL1049649848.2022.pdf1049649848.2022.pdfTesis de Maestría en Matemáticasapplication/pdf490740https://repositorio.unal.edu.co/bitstream/unal/82506/2/1049649848.2022.pdfbd155d7656731ab5c51477affb78df2aMD52THUMBNAIL1049649848.2022.pdf.jpg1049649848.2022.pdf.jpgGenerated Thumbnailimage/jpeg3721https://repositorio.unal.edu.co/bitstream/unal/82506/3/1049649848.2022.pdf.jpgd212618753293984969247f67fc0d0d5MD53unal/82506oai:repositorio.unal.edu.co:unal/825062024-08-12 02:00:17.205Repositorio Institucional Universidad Nacional de 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