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Le sujet principal de cette thèse est la distribution des nombres premiers dans les progressions arithmétiques, c'est-à-dire des nombres premiers de la forme $qn+a$, avec $a$ et $q$ des entiers fixés et $n=1,2,3,\dots$ La thèse porte aussi sur la comparaison de différentes suites arithmétiques par rapport à leur comportement dans les progressions arithmétiques. Elle est divisée en quatre chapitres et contient trois articles. Le premier chapitre est une invitation à la théorie analytique des nombres, suivie d'une revue des outils qui seront utilisés plus tard. Cette introduction comporte aussi certains résultats de recherche, que nous avons cru bon d'inclure au fil du texte. Le deuxième chapitre contient l'article \emph{Inequities in the Shanks-Rényi prime number race: an asymptotic formula for the densities}, qui est le fruit de recherche conjointe avec le professeur Greg Martin. Le but de cet article est d'étudier un phénomène appelé le <<Biais de Chebyshev>>, qui s'observe dans les <<courses de nombres premiers>>. Chebyshev a observé qu'il semble y avoir plus de premiers de la forme $4n+3$ que de la forme $4n+1$. De manière plus générale, Rubinstein et Sarnak ont montré l'existence d'une quantité $\delta(q;a,b)$, qui désigne la probabilité d'avoir plus de premiers de la forme $qn+a$ que de la forme $qn+b$. Dans cet article nous prouvons une formule asymptotique pour $\delta(q;a,b)$ qui peut être d'un ordre de précision arbitraire (en terme de puissance négative de $q$). Nous présentons aussi des résultats numériques qui supportent nos formules. Le troisième chapitre contient l'article \emph{Residue classes containing an unexpected number of primes}. Le but est de fixer un entier $a\neq 0$ et ensuite d'étudier la répartition des premiers de la forme $qn+a$, en moyenne sur $q$. Nous montrons que l'entier $a$ fixé au départ a une grande influence sur cette répartition, et qu'il existe en fait certaines progressions arithmétiques contenant moins de premiers que d'autres. Ce phénomène est plutôt surprenant, compte tenu du théorème des premiers dans les progressions arithmétiques qui stipule que les premiers sont équidistribués dans les classes d'équivalence $\bmod q$. Le quatrième chapitre contient l'article \emph{The influence of the first term of an arithmetic progression}. Dans cet article on s'intéresse à des irrégularités similaires à celles observées au troisième chapitre, mais pour des suites arithmétiques plus générales. En effet, nous étudions des suites telles que les entiers s'exprimant comme la somme de deux carrés, les valeurs d'une forme quadratique binaire, les $k$-tuplets de premiers et les entiers sans petit facteur premier. Nous démontrons que dans chacun de ces exemples, ainsi que dans une grande classe de suites arithmétiques, il existe des irrégularités dans les progressions arithmétiques $a\bmod q$, avec $a$ fixé et en moyenne sur $q$. / The main subject of this thesis is the distribution of primes in arithmetic progressions, that is of primes of the form $qn+a$, with $a$ and $q$ fixed, and $n=1,2,3,\dots$ The thesis also compares different arithmetic sequences, according to their behaviour over arithmetic progressions. It is divided in four chapters and contains three articles. The first chapter is an invitation to the subject of analytic number theory, which is followed by a review of the various number-theoretic tools to be used in the following chapters. This introduction also contains some research results, which we found adequate to include. The second chapter consists of the article \emph{Inequities in the Shanks-Rényi prime number race: an asymptotic formula for the densities}, which is joint work with Professor Greg Martin. The goal of this article is to study <<Chebyshev's Bias>>, a phenomenon appearing in <<prime number races>>. Chebyshev was the first to observe that there tends to be more primes of the form $4n+3$ than of the form $4n+1$. More generally, Rubinstein and Sarnak showed the existence of the quantity $\delta(q;a,b)$, which stands for the probability of having more primes of the form $qn+a$ than of the form $qn+b$. In this paper, we establish an asymptotic series for $\delta(q;a,b)$ which is precise to an arbitrary order of precision (in terms of negative powers of $q$). %(it can be instantiated with an error term smaller than any negative power of $q$). We also provide many numerical results supporting our formulas. The third chapter consists of the article \emph{Residue classes containing an unexpected number of primes}. We fix an integer $a \neq 0$ and study the distribution of the primes of the form $qn+a$, on average over $q$. We show that the choice of $a$ has a significant influence on this distribution, and that some arithmetic progressions contain, on average over q, fewer primes than typical arithmetic progressions. This phenomenon is quite surprising since in light of the prime number theorem for arithmetic progressions, the primes are equidistributed in the residue classes $\bmod q$. The fourth chapter consists of the article \emph{The influence of the first term of an arithmetic progression}. In this article we are interested in studying more general arithmetic sequences and finding irregularities similar to those observed in chapter three. Examples of such sequences are the integers which can be written as the sum of two squares, values of binary quadratic forms, prime $k$-tuples and integers free of small prime factors. We show that a broad class of arithmetic sequences exhibits such irregularities over the arithmetic progressions $a\bmod q$, with $a$ fixed and on average over $q$.

Le sujet principal de cette thèse est la distribution des nombres premiers dans les progressions arithmétiques, c'est-à-dire des nombres premiers de la forme $qn+a$, avec $a$ et $q$ des entiers fixés et $n=1,2,3,\dots$ La thèse porte aussi sur la comparaison de différentes suites arithmétiques par rapport à leur comportement dans les progressions arithmétiques. Elle est divisée en quatre chapitres et contient trois articles. Le premier chapitre est une invitation à la théorie analytique des nombres, suivie d'une revue des outils qui seront utilisés plus tard. Cette introduction comporte aussi certains résultats de recherche, que nous avons cru bon d'inclure au fil du texte. Le deuxième chapitre contient l'article \emph{Inequities in the Shanks-Rényi prime number race: an asymptotic formula for the densities}, qui est le fruit de recherche conjointe avec le professeur Greg Martin. Le but de cet article est d'étudier un phénomène appelé le <<Biais de Chebyshev>>, qui s'observe dans les <<courses de nombres premiers>>. Chebyshev a observé qu'il semble y avoir plus de premiers de la forme $4n+3$ que de la forme $4n+1$. De manière plus générale, Rubinstein et Sarnak ont montré l'existence d'une quantité $\delta(q;a,b)$, qui désigne la probabilité d'avoir plus de premiers de la forme $qn+a$ que de la forme $qn+b$. Dans cet article nous prouvons une formule asymptotique pour $\delta(q;a,b)$ qui peut être d'un ordre de précision arbitraire (en terme de puissance négative de $q$). Nous présentons aussi des résultats numériques qui supportent nos formules. Le troisième chapitre contient l'article \emph{Residue classes containing an unexpected number of primes}. Le but est de fixer un entier $a\neq 0$ et ensuite d'étudier la répartition des premiers de la forme $qn+a$, en moyenne sur $q$. Nous montrons que l'entier $a$ fixé au départ a une grande influence sur cette répartition, et qu'il existe en fait certaines progressions arithmétiques contenant moins de premiers que d'autres. Ce phénomène est plutôt surprenant, compte tenu du théorème des premiers dans les progressions arithmétiques qui stipule que les premiers sont équidistribués dans les classes d'équivalence $\bmod q$. Le quatrième chapitre contient l'article \emph{The influence of the first term of an arithmetic progression}. Dans cet article on s'intéresse à des irrégularités similaires à celles observées au troisième chapitre, mais pour des suites arithmétiques plus générales. En effet, nous étudions des suites telles que les entiers s'exprimant comme la somme de deux carrés, les valeurs d'une forme quadratique binaire, les $k$-tuplets de premiers et les entiers sans petit facteur premier. Nous démontrons que dans chacun de ces exemples, ainsi que dans une grande classe de suites arithmétiques, il existe des irrégularités dans les progressions arithmétiques $a\bmod q$, avec $a$ fixé et en moyenne sur $q$. / The main subject of this thesis is the distribution of primes in arithmetic progressions, that is of primes of the form $qn+a$, with $a$ and $q$ fixed, and $n=1,2,3,\dots$ The thesis also compares different arithmetic sequences, according to their behaviour over arithmetic progressions. It is divided in four chapters and contains three articles. The first chapter is an invitation to the subject of analytic number theory, which is followed by a review of the various number-theoretic tools to be used in the following chapters. This introduction also contains some research results, which we found adequate to include. The second chapter consists of the article \emph{Inequities in the Shanks-Rényi prime number race: an asymptotic formula for the densities}, which is joint work with Professor Greg Martin. The goal of this article is to study <<Chebyshev's Bias>>, a phenomenon appearing in <<prime number races>>. Chebyshev was the first to observe that there tends to be more primes of the form $4n+3$ than of the form $4n+1$. More generally, Rubinstein and Sarnak showed the existence of the quantity $\delta(q;a,b)$, which stands for the probability of having more primes of the form $qn+a$ than of the form $qn+b$. In this paper, we establish an asymptotic series for $\delta(q;a,b)$ which is precise to an arbitrary order of precision (in terms of negative powers of $q$). %(it can be instantiated with an error term smaller than any negative power of $q$). We also provide many numerical results supporting our formulas. The third chapter consists of the article \emph{Residue classes containing an unexpected number of primes}. We fix an integer $a \neq 0$ and study the distribution of the primes of the form $qn+a$, on average over $q$. We show that the choice of $a$ has a significant influence on this distribution, and that some arithmetic progressions contain, on average over q, fewer primes than typical arithmetic progressions. This phenomenon is quite surprising since in light of the prime number theorem for arithmetic progressions, the primes are equidistributed in the residue classes $\bmod q$. The fourth chapter consists of the article \emph{The influence of the first term of an arithmetic progression}. In this article we are interested in studying more general arithmetic sequences and finding irregularities similar to those observed in chapter three. Examples of such sequences are the integers which can be written as the sum of two squares, values of binary quadratic forms, prime $k$-tuples and integers free of small prime factors. We show that a broad class of arithmetic sequences exhibits such irregularities over the arithmetic progressions $a\bmod q$, with $a$ fixed and on average over $q$.

Made available in DSpace on 2016-04-27T16:58:29Z (GMT). No. of bitstreams: 1 Paulo Rogerio Salomao.pdf: 1515343 bytes, checksum: e8054aa96548e5060d5d9c759a64a899 (MD5) Previous issue date: 2007-10-02 / In the first term of 2005, I joined the Professional Master s degree on Mathematics Teaching at PUC/SP. In this same year, the research project AProvaME, whose goals are: investigating concepts about argumentation and proofs of teenager students at schools from São Paulo state; structuring groups composed by teachers and researchers in order to elaborate activities involving students in the building process of knowledge, arguments and proofs in Mathematics, the use of technology and the investigating the teacher s role as the mediator of this process. As a part of this project, I will structure my dissertation in order to investigate two situations. The first one to verify to what extent, by the teacher s mediation and by the activities proposed, it is possible to engage students in argument, justification and proof of conjectures about Arithmetical Progressions. On the second one, investigating if the use of technology can favor the building of arguments, justification and proofs in Arithmetical Progressions by the students. Oriented by these questions, I tried to raise some observations of how the teacher s mediation should be done, using activities related to Arithmetical Progressions to engage the students in argument, justifying and proof situations, as well as which type and how to use the technologies available: first of all, I realized the need for the teacher s mediation after each ending of a group of activities, making a closure, or else, proposing to the students that they needed to confront and discuss, giving arguments, justifying their answers, so that everyone could proceed to the following activities without compromising their conjectures; subsequently; I verified that the use of technology is an incentive to the performing of activities in any area of knowledge, because the students feel motivated to build geometrical figures in the computer to solve the Mathematics exercises, concluding, with relation to the use of technology, I noticed that in the activities of this essay the usage of one more computational tool for the validation of students answers, as the Excel software, could complement the results obtained. This essay was based, mainly on the nine types of tasks extracted from Balacheff et al. text (2001). The methodology used was the teaching experiment, always looking for an improvement, not only in the activity, but also in the teacher-studenttechnology interaction. The research involved 10th graders from the evening shift of a State public network school / No primeiro semestre de 2005, ingressei no curso de Mestrado Profissional em Ensino de Matemática na PUC/SP. Neste mesmo ano, iniciava-se o projeto de pesquisa AProvaME, cujos objetivos são: investigar concepções sobre argumentação e prova de alunos adolescentes em escolas do Estado de São Paulo; formar grupos compostos por professores e pesquisadores para elaboração de atividades envolvendo alunos em processos de construção de conhecimento, argumentos e provas em Matemática e o uso de tecnologia e investigar o papel do professor como mediador neste processo. Por fazer parte deste projeto, estruturarei minha dissertação para investigar duas situações. A primeira para verificar em que medida, por meio da mediação do professor e das atividades propostas, é possível engajar os alunos em situações de argumentar, justificar e provar conjecturas sobre Progressões Aritméticas. Na segunda, investigar se o uso de tecnologia pode favorecer a construção de argumentos, justificativas e provas em Progressões Aritméticas pelos alunos. Orientado por essas questões, procurei levantar algumas observações de como deve ser feita a mediação do professor, utilizando atividades de Progressões Aritméticas para engajar os alunos em situações de argumentações, justificativas e provas, bem como qual tipo e como usar as tecnologias disponíveis: em primeiro lugar, percebi a necessidade da mediação do professor a cada término de atividade ou a cada final de um grupo de atividades, fazendo um fechamento, ou seja, propondo que os alunos confrontassem e discutissem, argumentando e justificando suas respostas, para que todos pudessem prosseguir com as atividades seguintes sem comprometimento de suas conjecturas; em seguida, verifiquei que o uso de tecnologia é um incentivo para a realização de atividades em qualquer área do conhecimento, pois os alunos sentem-se motivados por construir figuras geométricas no computador para a resolução de exercícios de Matemática; ao finalizar, com relação ao uso da tecnologia, constatei que nas atividades deste trabalho a utilização de mais uma ferramenta computacional para validação das respostas dos alunos, como o software Excel, poderia complementar os resultados obtidos. Este trabalho fundamentou-se, sobretudo nos nove tipos de tarefas extraídos do texto de Balacheff et al. (2001). A metodologia utilizada foi o experimento de ensino, objetivando sempre um aperfeiçoamento, tanto das atividades, como da interação professor aluno tecnologia. A pesquisa envolveu oito alunos da 1ª série do Ensino Médio do período noturno de uma escola da rede pública estadual

La present tesi avalua les diferències entre homes i dones quant a les característiques sociodemogràfiques i clínicopatològiques, procés diagnòstic, tractament i pronòstic en una sèrie de casos diagnosticats de novo de càncer de bufeta en 18 hospitals de 5 regions espanyoles (estudi EPICURO). També s'estudia l'associació entre tabac i risc de càncer de bufeta segons el sexe en un estudi agregat d'estudis cas-control europeus i nord-americans de càncer de bufeta.Es trobaren diferències entre sexes quant a la incidència de la malaltia, en algunes característiques anatomopatològiques dels tumors i quant a tractament. No es varen observar diferències entre sexes davant d'un mateix nivell d'exposició al tabac. També s'observaren diferències entre homes i dones quant al risc de recidivar i de progressar dels tumors vesicals superficials, però no en el risc de morir dels pacients amb tumors invasius. / The thesis evaluates differences related to sociodemographic and clinic-pathological characteristics, diagnostic tests, treatment and prognosis of bladder cancer patients newly diagnosed in 18 hospitals from 5 Spanish areas according to sex. The work also assess the association between tobacco and bladder cancer risk according to sex in a pooled analysis of case-control studies of bladder cancer from Europe and North America.Differences between sex concerning disease incidence, pathological characteristics and treatment were observed. The relative risk of bladder cancer associated with tobacco was similar in both sex. Differences between men and women were observed regarding risk of recurrence and progression of their superficial tumors but not regarding risk of death because of an invasive tumor.

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2015-10-22T14:20:36Z No. of bitstreams: 2 Dissertação - Alexandre Carlos da Silva Teixeira - 2015.pdf: 5570395 bytes, checksum: 56c1a16748accf85c9390695464810aa (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-10-22T14:22:35Z (GMT) No. of bitstreams: 2 Dissertação - Alexandre Carlos da Silva Teixeira - 2015.pdf: 5570395 bytes, checksum: 56c1a16748accf85c9390695464810aa (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2015-10-22T14:22:35Z (GMT). No. of bitstreams: 2 Dissertação - Alexandre Carlos da Silva Teixeira - 2015.pdf: 5570395 bytes, checksum: 56c1a16748accf85c9390695464810aa (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2015-06-26 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This paper presents a proposal for relationship studies between mathematics and music, a relationship that has been established since the dawn of humanity, and could be seen more clearly from the studies developed by Pythagoras. We approach the evolution of music in the historical context and introduce the basics of music theory, essential to establishing relationships with mathematics. Our e orts were focused on instruments with strings, by which present a relationship between a musical scale, called Chromatic and geometric progressions; also we present a relationship between musical intervals and right triangles. We present a mathematical relationship between music and colors, through their respective frequencies of sound and light. Also we address the present mathematics in the construction of some instruments with strings, via Golden Proportion, and nished the work presented some proposals for activities that can be worked in the classroom, aimed at high school students. / Este trabalho traz uma proposta de estudos da relação existente entre a Matemática e a Música, relação esta que foi estabelecida desde os primórdios da humanidade, e pôde ser observada de forma mais clara a partir dos estudos desenvolvidos por Pitágoras. Abordamos a evolução da Música no contexto histórico e introduzimos as noções básicas de teoria musical, essencial ao estabelecimento de relações com a Matemática. Nossos esforços foram focados nos instrumentos com cordas, pelos quais apresentamos uma relação entre uma escala musical, denominada Cromática, e as progressões geométricas; também apresentamos uma relação entre intervalos musicais e os triângulos retângulos. Apresentamos uma relação matemática entre a Música e as cores, por meio de suas respectivas frequências de som e luz. Também abordamos a matemática presente na construção de alguns instrumentos com cordas, via Proporção Áurea, e nalizamos o trabalho apresentando algumas propostas de atividades que podem ser trabalhadas em sala de aula, voltadas para alunos do Ensino Médio.