Global ETD Search

1	DIAGONAL FORMS AND THE RATIONALITY OF THE POINCARÉ SERIES Deb, Dibyajyoti 01 January 2010 (has links) 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. number theory Poincaré series diagonal forms p-adic numbers Mathematics
2	ON P-ADIC FIELDS AND P-GROUPS Sordo Vieira, Luis A. 01 January 2017 (has links) The dissertation is divided into two parts. The first part mainly treats a conjecture of Emil Artin from the 1930s. Namely, if f = a_1x_1^d + a_2x_2^d +...+ a_{d^2+1}x^d where the coefficients a_i lie in a finite unramified extension of a rational p-adic field, where p is an odd prime, then f is isotropic. We also deal with systems of quadratic forms over finite fields and study the isotropicity of the system relative to the number of variables. We also study a variant of the classical Davenport constant of finite abelian groups and relate it to the isotropicity of diagonal forms. The second part deals with the theory of finite groups. We treat computations of Chermak-Delgado lattices of p-groups. We compute the Chermak-Delgado lattices for all p-groups of order p^3 and p^4 and give results on p-groups of order p^5. p-adic fields diagonal forms unramified extensions additive equations number theory Algebra Number Theory
3	Two Cases of Artin's Conjecture Kaesberg, Miriam Sophie 18 December 2020 (has links) No description available. 510 $p$-adic solutions Artin's conjecture Diagonal forms Additive forms Pairs of forms Cubic forms Solutions in $\mathbb{Q}_p$ Analytic number theory Diophantine equations in many variables Congruences in many variables Mathematik (PPN61756535X)

1

Page generated in 0.0781 seconds