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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Pares de formas aditivas e a conjectura de Artin

Souza Neto, Tertuliano Carneiro de 28 February 2011 (has links)
Tese (doutorado)—Universidade de Brasília, Instituto de Ciências Exatas, Departamento de Matemática, 2011. / Submitted by wiliam de oliveira aguiar (wiliam@bce.unb.br) on 2011-06-27T17:20:02Z No. of bitstreams: 1 2011_TertulianoCarneirodeSouzaNeto.pdf: 489280 bytes, checksum: c757fc5257dd8408cbf6a1d641c6cbee (MD5) / Approved for entry into archive by Repositorio Gerência(repositorio@bce.unb.br) on 2011-06-30T17:50:48Z (GMT) No. of bitstreams: 1 2011_TertulianoCarneirodeSouzaNeto.pdf: 489280 bytes, checksum: c757fc5257dd8408cbf6a1d641c6cbee (MD5) / Made available in DSpace on 2011-06-30T17:50:48Z (GMT). No. of bitstreams: 1 2011_TertulianoCarneirodeSouzaNeto.pdf: 489280 bytes, checksum: c757fc5257dd8408cbf6a1d641c6cbee (MD5) / Seja f(x1, ..., xn) = a1xk 1 + ... + anxk n g(x1, ..., xn) = b1xk 1 + ... + bnxk n (1) um par de formas aditivas de grau pΤ (p − 1). Estamos interessados em obter condições que garantam a existência de zeros p-ádicos para o par (1). Uma conhecida conjectura, devida a Emil Artin, afirma que a condição n > 2k2 é suficiente. Utilizando técnicas da Teoria Combinatória dos Números, provamos que a condição n > 2 p (p/ P – 1) k2 − 2k é suficiente se k = 2.3Τ ou 4.5Τ, e em qualquer caso se Τ≥ (p – 1)/ 2. _____________________________________________________________________________________ ABSTRACT / Let f(x1, ..., xn) = a1xk 1 + ... + anxk n g(x1, ..., xn) = b1xk 1 + ... + bnxk n (1) be a pair of additive forms of degree pΤ (p − 1). We are interested in finding conditions which guarantee the existence of p-adic zeros to the pair (2). A well-known conjecture due to Emil Artin states that the condition n > 2k2 is sufficient. By means of techniques of Combinatorial Number Theory, we prove that n > 2 p (p/ P – 1) k2 − 2k is sufficient if k = 2.3Τ ou 4.5Τ, and in any case if Τ≥ (p – 1)/ 2.
2

A confirmação da Conjectura de Artin para pares de formas aditivas de graus 2T.3 e 3T.2

Ventura, Luciana Lima 28 February 2013 (has links)
Tese (doutorado)—Universidade de Brasília, Instituto de Ciências Exatas, Departamento de Matemática, 2013. / Submitted by Albânia Cézar de Melo (albania@bce.unb.br) on 2013-09-09T14:24:13Z No. of bitstreams: 1 2013_LucianaLimaVentura.pdf: 572550 bytes, checksum: 0ce7cf628a3d83b89a7518122378820d (MD5) / Approved for entry into archive by Guimaraes Jacqueline(jacqueline.guimaraes@bce.unb.br) on 2013-09-09T15:46:43Z (GMT) No. of bitstreams: 1 2013_LucianaLimaVentura.pdf: 572550 bytes, checksum: 0ce7cf628a3d83b89a7518122378820d (MD5) / Made available in DSpace on 2013-09-09T15:46:43Z (GMT). No. of bitstreams: 1 2013_LucianaLimaVentura.pdf: 572550 bytes, checksum: 0ce7cf628a3d83b89a7518122378820d (MD5) / Uma versão da Conjectura de Artin afirma que para um sistema homogêneo com duas equações diagonais de grau k, cujos coeficientes são inteiros, ter solução p-ádica não trivial é suficiente que o número de variáveis seja maior que 2 k2. Nesse trabalho, vamos mostrar que a conjectura é verdadeira quando o grau é 2T . 3 ou 3T . 2, para T≥ 2. ______________________________________________________________________________ ABSTRACT / One version of Artin's Conjecture states that for a homogeneous system with two diagonal equations of degree k, whose coe cients are integers, exists a nontrivial p-adic solution provided the number of variables is greater than 2 k2. In this paper, we show that the conjecture is true when the degree is 2T . 3 or 3T . 2, for T≥ 2.
3

Survey on special values of Artin L-function.

January 1991 (has links)
by Ka-hon Yeung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1991. / Bibliography: leaves 155-158. / Chapter 1) --- INTRODUCTION --- p.1 / Chapter 2) --- BACKGROUND MATERIALS AND DEFINITIONS --- p.3 / Chapter §1. --- THE RIEMANN ZETA FUNCTION --- p.3 / Chapter §2. --- THE DEDEKIND ZETA FUNCTION --- p.9 / Chapter §3. --- THE DIRICHLET L-FUNCTION --- p.11 / Chapter §4. --- PLACES AND ABSOLUTE VALUES --- p.13 / Chapter §5. --- THE HECKE L-FUNCTION --- p.14 / Chapter §6. --- CLASS FIELD THEORY --- p.17 / Chapter §7. --- LINEAR REPRESENTATIONS OF FINITE GROUPS --- p.19 / Chapter §8. --- THE ARTIN L-FUNCTION --- p.22 / Chapter 3) --- WORKS OF VARIOUS PEOPLE IN THE EVALUATION OF L-FUNCTIONS --- p.28 / Chapter §1. --- CLASS NUMBER FORMULA --- p.28 / Chapter §2. --- WORKS OF SHINTANI --- p.35 / Chapter §3. --- WORKS OF STARK --- p.65 / Chapter 4) --- STARK'S CONJECTURE --- p.90 / Chapter § 1. --- WORKS OF STARK --- p.90 / Chapter §2. --- WORKS OF TATE --- p.102 / Chapter §3. --- WORKS OF SANDS --- p.132 / NOTE --- p.146 / APPENDIX --- p.153 / BIBLIOGRAPHY --- p.155

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