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Showing 1 to 17 of 17 for “"Algebraic number theory"”.
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Special Cases of Density Theorems in Algebraic Number Theory
This paper discusses the concepts in algebraic and analytic number theory used in the proofs of Dirichlet's and Cheboterev's density theorems. It presents special cases of results due to the latter theorem for which greatly simplified proofs exist.
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Integral Basis For Pure Cubic Fields
… fields is determined using known results of algebraic number theory.
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The zeta function of an order in a general algebra
Zeta functions have been of major importance in algebraic number theory for many years. They are useful (along with L-functions) in obtaining results concerning the asymptotic distribution of ideals in a given class. In 1980 Bushnell and Reiner were able to extend these classical results to the …
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Fourier Coefficients of Modular Forms and Their Applications
The theory of modular forms, as it has been developed over the past several decades, has highlighted deep connections between the areas of analytic and algebraic number theory and arithmetic geometry. In this thesis we explore some applications. First, we give some new and simpler proofs of recent …
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The Birch and Swinnerton-Dyer Conjecture for elliptic curves
… in modern Mathematics. A review of topics in Algebraic Number Theory and Algebraic Geometry is provided in order to provide a characterisation for elliptic curves over rational numbers. We investigate the group structure of rational points on elliptic curves, and show that this group is …
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Case studies of employee participation programs in construction and their effects on absenteeism
In recent years, the construction industry has shown a steady decline in productivity and worker morale, while experiencing an increase in absenteeism (Maloney, 1991; CII, 1982). This has had a tremendous economic and motivational impact. This dilemma coupled with the fast-paced growth of …
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Relative oriented class groups of quadratic extensions
… groups associated to quadratic extensions of number fields L/K, extending work of Bhargava concerning composition laws for binary quadratic forms over number fields of higher degree. This work generalized the classical correspondence between ideal classes of quadratic orders and classes of …
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Non-Asymptotic 𝑡-Wise Independence of Substitution-Permutation Networks
… particular, we use exponential sums results from algebraic number theory to show that 7𝑡+𝑜(𝑡) rounds of MiMC on a prime order field are 𝑡-wise independent. This result is tight up to constant factors and is the first proof of 𝑡-wise independence for any concrete cipher.
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Determination of Quadratic Lattices by Local Structure and Sublattices of Codimension One
… quadratic lattices over the rings of integers of algebraic number fields, it is shown that lattices are determined up to isometry by their local structure and sublattices of codimension 1. In particular, a theorem of Yoshiyuki Kitaoka for $\mathbb{Z}$-lattices is generalized to definite lattices …
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Approximate converse theorem
The theme of this thesis is an "approximate converse theorem" for globally unramified cuspidal representations of PGL(n, A), n ≥ 1. For a given set of Langlands parameters for some places of Q, we can compute ε > 0 such that there exists a genuine globally unramified cuspidal representation, whose …
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Abelian groups formed by reisdues with respect to a double modulus
Made available in DSpace on 2016-11-09T23:47:27Z (GMT). No. of bitstreams: 2 5977878_opt.pdf: 690172 bytes, checksum: 7b94297e64df09b07a98b89c8419212c (MD5) license.txt: 4183 bytes, checksum: 1dcc2037833d76bede73d5717587543b (MD5) Previous issue date: 1912
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An Introduction to the General Number Field Sieve
… the RSA system would be nullified. The General Number Field Sieve algorithm is the fastest known method for factoring large integers. Research and development of this algorithm within the past five years has facilitated factorizations of integers that were once speculated to require thousands of …
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An Algebraic Circle Method
… Circle Method to give estimates for the number of curves in a variety over a finite field. The key step in the classical Circle Method is to prove that some cancellation occurs in some exponential sums. Using a theorem of Katz, we reduce this to bounding the dimension of some singular …
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Equivariance in Tannakian duality and plectic p-adic Hodge theory
… We then study a plectic variant of Fontaine theory for p-adic representations of the local plectic Galois group at p associated to a totally real number field F, when p is inert in F. In particular, we show that the plectic crystalline Fontaine functor is valued in a category of plectic …
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MONOID RINGS AND STRONGLY TWO-GENERATED IDEALS
<p>This paper determines whether monoid rings with the two-generator property have the strong two-generator property. Dedekind domains have both the two-generator and strong two-generator properties. How common is this? Two cases are considered here: the zero-dimensional case and the …
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ON ASAI’S FUNCTION ANALOGOUS TO log |η(z)|
… to Eisenstein series of level one defined for a number field with class number one and obtained a function analogous to the logarithm of the absolute value of the eta function. In this thesis we reformulate Asai’s function adelically using the theory of admissible representations for GL2 and …