Bibliographies: leaves ii & 146-150.

Thesis (Ph. D.)--University of Idaho, 2006. / Abstract. "April 2006." Includes bibliographical references (leaf 69). Also available online in PDF format.

The Poincaré series, Py(f) of a polynomial f was first introduced by Borevich and Shafarevich in [BS66], where they conjectured, that the series is always rational. Denef and Igusa independently proved this conjecture. However it is still of interest to explicitly compute the Poincaré series in special cases. In this direction several people looked at diagonal polynomials with restrictions on the coefficients or the exponents and computed its Poincaré series. However in this dissertation we consider a general diagonal polynomial without any restrictions and explicitly compute its Poincaré series, thus extending results of Goldman, Wang and Han. In a separate chapter some new results are also presented that give a criterion for an element to be an mth power in a complete discrete valuation ring.

Thesis (M. Sc.)--University of Adelaide, 1979. / Bibliographies: leaves ii & 146-150.

Let K be an imaginary quadratic field, with associated quadratic character α. We construct an analytic p-adic L-function interpolating the special values L(1, ad(f) ⊗ α) as f varies in a Hida family; these values are non-critical in the sense of Deligne. Our approach is based on Greenberg--Stevens' idea of Λ-adic modular symbols. By considering cohomology with values in a space of p-adic measures, we construct a Λ-adic evaluation map that interpolates Hida's integral expression as the weight varies. The p-adic L-function is obtained by applying this map to a cohomology class corresponding to the given Hida family.

This thesis introduces the p-adic metric on the rational numbers. We then present the basic properties of this metric. Using this metric, we explore conic sections, viewed as equidistant sets. Lastly, we move on the sequences and series, and from there, we define p-adic expansions and the analytic completion of Q with respect to the p-adic metric, which leads to exploring some arithmetic properties of Qp.

Submitted by Erika Demachki (erikademachki@gmail.com) on 2014-09-18T20:04:19Z No. of bitstreams: 2 DISSERT.CORRETA.DAI.pdf: 1217710 bytes, checksum: dd809f01ecd6c0000cfa17badb034cf1 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Rejected by Luciana Ferreira (lucgeral@gmail.com), reason: Há problemas nos campos de palavras chaves e citação. 11º. Palavras chaves só use a primeira letra maiúscula de cada palavra chave, e caso não tenha unitermo no resumo use as palavras chaves da ficha catalográfica, mas como unitermo, ou seja, palavras isoladas. Coloque, também, o correspondente das palavras chaves em inglês, a menos que não tenha na dissertação ou tese Ex.: Controle de qualidade Atividade antimicrobiana Qualitycontrol Antimicrobial activity A citação tem que ser adequada a NBR 6023. Ex.: ALCÂNTARA, Guizelle Aparecida de. Caracterização farmacognostica e atividade antimicrobiana da folha e casca do caule da myrciarostratadc.(myrtaceae). 2012. 41 f. Dissertação (Mestrado em Ciências Farmacêuticas) - Universidade Federal de Goiás, Goiânia, 2012. on 2014-09-19T13:15:04Z (GMT) / Submitted by Erika Demachki (erikademachki@gmail.com) on 2014-09-22T18:09:15Z No. of bitstreams: 2 DISSERT.CORRETA.DAI.pdf: 1217710 bytes, checksum: dd809f01ecd6c0000cfa17badb034cf1 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Jaqueline Silva (jtas29@gmail.com) on 2014-09-22T19:11:21Z (GMT) No. of bitstreams: 2 DISSERT.CORRETA.DAI.pdf: 1217710 bytes, checksum: dd809f01ecd6c0000cfa17badb034cf1 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2014-09-22T19:11:21Z (GMT). No. of bitstreams: 2 DISSERT.CORRETA.DAI.pdf: 1217710 bytes, checksum: dd809f01ecd6c0000cfa17badb034cf1 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2013-03-21 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This work is based on articles by Atkinson, and Cook Brüdern [2] and I. D. Meir [15] treating solubility p-adic nontrivial of the systems for additive equations of degree k in n variables. Using techniques of the exponential sums we will see that to ensure the solubility nontrivial of such systems when p > k2r+2, then 2rk + 1 variables will be sufficient. When p > r2k2+2/(c−2) e r 6= 1 then n > crk variables are sufficient. In the case where r = 1 we assure solubility nontrivial p-adic for every p > k2+2/(c−1). / Este trabalho é baseado nos artigos de Atkinson, Brüdern e Cook [2] e I. D. Meir [15] que tratam de solubilidade p-ádica não trivial para sistemas de equações aditivas de grau k em n variáveis. Usando técnicas de somas exponenciais veremos que para garantir a solubilidade não trivial de tais sistemas quando p > k2r+2, então 2rk+1 variáveis serão suficientes. Quando p > r2k2+2/(c−2) e r 6= 1 então n > crk variáveis são suficientes. No caso em que r = 1 garantimos a solublidade não trivial p-ádica para todo p > k2+2/(c−1).

Newton polygons are constructions over the p-adic numbers used to find information about the roots of a polynomial or power series. In this the- sis, we will first investigate the construction of the field Qp on the p-adic numbers. Then, we will use theorems such as Eisenstein’s Irreducibility Criterion, Newton’s Method, Hensel’s Lemma, and Strassman’s Theorem to build and justify Newton polygons.

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This paper presents the theory of Secondary Representation of modules over a commutative ring and their Attached Primes; introduced in 1973 by I. MacDonald as a dual to the important theory of associated primes and primary decomposition in commutative algebra. The paper explores many of the basic aspects of the theory of primary decomposition and associated primes of modules in the hopes to delineate and motivate the construction of a secondary representation, when possible. The thesis discusses the results of the uniqueness of representable modules and their attached primes, and, in particular, the existence of a secondary representation for Artinian modules. It concludes with some interesting examples of both secondary and representable modules, highlighting the consequences of the results thus established.