{"id":117915,"date":"2018-03-11T10:47:38","date_gmt":"2018-03-11T10:47:38","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/sobre-los-ceros-de-polinomios-de-dirichlet-en-general-y-los-de-las-sumas-parciales-de-la-funcion-zeta-de-riemann-en-particular\/"},"modified":"2018-03-11T10:47:38","modified_gmt":"2018-03-11T10:47:38","slug":"sobre-los-ceros-de-polinomios-de-dirichlet-en-general-y-los-de-las-sumas-parciales-de-la-funcion-zeta-de-riemann-en-particular","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/analisis-y-analisis-funcional\/sobre-los-ceros-de-polinomios-de-dirichlet-en-general-y-los-de-las-sumas-parciales-de-la-funcion-zeta-de-riemann-en-particular\/","title":{"rendered":"Sobre los ceros de polinomios de dirichlet, en general, y los de las sumas parciales de la funci\u00f3n zeta de riemann, en particular"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Eric Vincent Dubon <\/strong><\/h2>\n<p>En el primer cap\u00edtulo se introduce la funci\u00f3n $h_{n}(z)=1+2^{iz}+3^{iz}+&#8230;+N^{iz}$ como aproximaci\u00f3n de la funci\u00f3n zeta de riemann y se pondr\u00e1 de relieve una de sus principales propiedades, que es la de ser una funci\u00f3n entera de tipo exponencial de clase c. Se presenta, utilizando la noci\u00f3n de distribuci\u00f3n de levinson, una demostraci\u00f3n de la densidad de ceros de este tipo de funciones distinta a la obtenida por los autores de [41]. Se dar\u00e1 tambi\u00e9n, con la condici\u00f3n de existencia de ceros sobre el eje imaginario, una f\u00f3rmula sobre la distribuci\u00f3n de dichos ceros. Despu\u00e9s, se presentan algunos resultados sobre el n\u00famero de ceros dentro de rect\u00e1ngulos de aproximaciones de la funci\u00f3n zeta de riemann y se expone c\u00f3mo el uso de la funci\u00f3n $h_{n}(z)$ permite obtener una f\u00f3rmula precisa del n\u00famero de ceros dentro de ciertos rect\u00e1ngulos.  en el segundo cap\u00edtulo se demuestra que para unas ciertas aproximaciones de la zeta de riemann, es decir, las sumas parciales, hay densidad de las partes reales de sus ceros simples dentro de intervalos incluidos en sus bandas cr\u00edticas. Los resultados de este cap\u00edtulo aparecen en [14].  en el tercer cap\u00edtulo se propone, utilizando aritm\u00e9tica y funciones completamente multiplicativas, un m\u00e9todo para transportar una propiedad topol\u00f3gica de ceros de ciertos polinomios exponenciales, llamados polinomios de dirichlet. Se utiliza el teorema de equiValencia de bohr, muy conocido para las series de dirichlet. Se demuestra que se puede aplicar este resultado a los polinomios de dirichlet, lo cual nos da un m\u00e9todo expl\u00edcito para construir polinomios obteniendo la propiedad requerida y formando, al mismo tiempo, clases de equiValencia.  en el cuarto cap\u00edtulo, despu\u00e9s de haber introducido el tema de las cuerdas fractales no reticulares, se demuestran conjeturas expuestas por michel lapidus y machiel van frankenhuysen en [30],  relacionadas con la densidad de las partes reales de ceros de polinomios de dirichlet asociados a dichas cuerdas. Se puede encontrar estos resultados en [13].  en el \u00faltimo cap\u00edtulo se exponen algunos resultados sobre la relaci\u00f3n entre los polinomios de dirichlet y las ecuaciones en diferencias de tipo neutro. Demostramos un resultado de inestabilidad para dichas ecuaciones y, utilizando el resultado anterior, se propone la creaci\u00f3n de  clases de equiValencias de ecuaciones en diferencias inestables.  al final de cada cap\u00edtulo, se presentan algunos temas abiertos que podr\u00edan ser desarrollados en el futuro.    in the first one we introduce the function $h_{n}(z)=1+2^{iz}+3^{iz}+&#8230;+N^{iz}$ as an approximation of the riemann&apos;s zeta function and we focus on one of its most important properties, which is to be an entire function of exponential type of $mathcal{c}$ class. We present, using the levinson&apos;s notion of distribution, a demonstration of the density of the zeros of such functions. This proof is different to the authors one (see [41]). We also give a formula of the distribution of zeros on the imaginary axis (if they exist). Then, we show some results on the number of zeros in rectangles of approximations of the riemann&apos;s zeta function and we will show how the use of the function $h_{n}(z)$ gives us a precise formula on the number of zeros in some specific rectangles.  in the second chapter we prove that for some particular approximations of the riemann&apos;s zeta functions, i. E., The partial sums, there is density in the real parts of its simple zeros in some intervals of their respective critical strips. The results of this chapter can be found in [14].  in the third chapter, using arithmetic and completely multiplicative functions, we offer a method to carry a topological property of the zeros of some exponential polynomials named dirichlet polynomials. We use the bohr-equivalence theorem which is usually used for dirichlet series. We show that we can use it for dirichlet poynomials too and we obtain an explicit method to construct polynomials with the desired property.  in the fourth chapter we introduce the notion of nonlattice fractal strings and then we prove the conjetures of michel lapidus and machiel van frankenhuysen (see [30]), which have a relation with the density of the real parts of the zeros of dirichlet polynomials associated to such strings. These results appear in [13].  in the last chapter we present some results on the relation between dirichlet polynomials and differential equations in differences of neutral type. We prove a result on unstability for such equations and using the previous result we will create some equivalent classes of differential equations with unstability.  at the end of each chapter, we present some open problems which could be further developed in future research<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Sobre los ceros de polinomios de dirichlet, en general, y los de las sumas parciales de la funci\u00f3n zeta de riemann, en particular<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Sobre los ceros de polinomios de dirichlet, en general, y los de las sumas parciales de la funci\u00f3n zeta de riemann, en particular <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Eric Vincent Dubon <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Murcia<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 17\/07\/2015<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Direcci\u00f3n y tribunal<\/h3>\n<ul>\n<li><strong>Director de la tesis<\/strong>\n<ul>\n<li>Angel Ferrandez Izquierdo<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: manuel L\u00f3pez pellicer <\/li>\n<li>Antonio Avil\u00e9s l\u00f3pez (vocal)<\/li>\n<li>alma Luisa Albujer brotons (vocal)<\/li>\n<li>Jes\u00fas Yepes nicolas (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Eric Vincent Dubon En el primer cap\u00edtulo se introduce la funci\u00f3n $h_{n}(z)=1+2^{iz}+3^{iz}+&#8230;+N^{iz}$ como aproximaci\u00f3n de la funci\u00f3n [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center 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