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Conjectura de Artin para pares de formas aditivas de grau 6 / Artin’s conjecture for pairs of additive sextic formsCelis Cerón, M.A 25 April 2014 (has links)
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Dissertaçao - Mónica Andrea Celis Cerón - 2014.pdf: 566862 bytes, checksum: b41da2ec2c63c537f6b78488d3d8c179 (MD5)
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Previous issue date: 2014-04-25 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Celis Cerón, Mónica Andrea. Artin’s conjecture for pairs of additive sextic forms. Goiânia, 2014. 62p. MSc. Dissertation. Instituto de Matemática e Estatística, Universidade Federal de Goiás.
Consider the system of equations
a1xk1+ a2xk2+ + asxks= 0;
b1xk1+ b2xk2+ + bsxks= 0;
where a1; a2; ; as; b1; b2; ; bs 2 Z
A special case of Artin’s conjecture states that the above system must have nontrivial
solutions in every p-adic field, Qp, provided only that s 2k2+ 1. In this text we show
that the conjecture is true when k = 6. / Celis Cerón, Mónica Andrea. Conjectura de Artin para pares de formas aditivas de grau 6. Goiânia, 2014. 62p. Dissertação de Mestrado. Instituto de Matemática e Estatística, Universidade Federal de Goiás.
Consideremos o sistema de equações
a1xk1+ a2xk2+...+ asxks= 0;
b1xk1+ b2xk2+ + bsxks= 0;
onde, a 1; a 2; ; as; b1; b2; ; bs 2 Z.
Um caso especial da conjectura de Artin nos diz que o sistema anterior tem solução não trivial em todo corpo p-ádico, Qp, sempre que s 2k2+ 1. Neste trabalho mostraremos que a conjectura é válida quando k = 6.
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Uma confirmação da conjectura de Artin para pares de formas diagonais de graus 2 e 3Lelis, Jean Carlos Aguiar 10 November 2015 (has links)
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Previous issue date: 2015-11-10 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work we present some methods used in the study of systems of additive forms
on local fields, and a proof for a particular case of Artin’s Conjecture, which says that
every systems with R additive forms of degrees k1; :::;kR has non trivial p-adic solution
for any prime p, if the number s of variables is higher than k2
1 +k2
2 + +k2R, given by
Wooley [12], where he shows that G(3;2) = 11.
Keywords / Nesse trabalho, nós apresentamos alguns dos métodos usados no estudo de formas
aditivas sobre corpos locais, e uma prova para um caso particular da Conjectura de
Artin, que afirma que todo sistema de R formas aditivas de graus k1;k2; :::;kR possui
solução p-ádica não trivial para todo p primo, se o número s de variáveis for maior que
k2
1 +k2
2 + +k2R
, dada por Wooley [12], onde ele mostra que G(3;2) = 11.
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