Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
Results
Showing 1 to 20 of 45 for “"Number fields"”.
-
Trinomials Defining Quintic Number Fields
Given a number field $K$, how does one find polynomials $f(x)$,
-
Irreducible elements in algebraic number fields
… involving irreducible elements in algebraic number fields. The first question is: Given an algebraic integer β in a field with class number greater than two, how many different lengths of factorizations into irreducibles exist? The distribution into ideal classes of the prime ideals whose …
-
Diophantine Avoidance, Number Fields, and Quadratic Forms
… investigation is to small-height generators of number fields satisfying certain natural avoidance conditions. Further, we study small-size integer zeros of integral quadratic forms with avoidance conditions. We apply our results to the problem of effective distribution of angles between vectors …
-
Link complements and imaginary quadratic number fields
Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1981.
-
Genus Fields and Central Extensions of Number Fields
… (narrow) genus group of an abelian extension of number fields using a four term exact sequence of abelian groups derived from work of Frohlich. There are two main results. First, if L/K is a cyclic l-extension, where l is a prime not dividing h(,K)('+), the narrow class number of K, then we …
-
The Easier Waring Problem in Algebraic Number Fields
Made available in DSpace on 2014-12-05T21:50:14Z (GMT). No. of bitstreams: 1 5904574.pdf: 1276509 bytes, checksum: 6bb5098e6f862d25b492f5a5a5e34a12 (MD5) Previous issue date: 1959
-
Local Conjugations of Groups and Applications to Number Fields
… of local conjugacy have been discovered. In number theory, the groups H, H', G appear as Galois groups of field extensions of the field of algebraic number field k, and H, H' are locally conjugate in G if and only if the fixed fields K, K' of H, H' have identical Dedekind zeta functions. In …
-
Massey products in the Galois cohomology of number fields
… group of the p-class field tower of a quadratic number field. This relation structure is described in terms of Massey products in the Galois cohomology of number fields. A connection is given to Milnor invariants and Redei symbols. In particluar, we prove a number theoretic analogue of the …
-
Maximal 2-Extensions of Number Fields With Limited Ramification
Let K be a number field, p a rational prime, and S a finite set of primes of K, none of which lies above p. Let K S be the maximal pro-p extension of K unramified outside S, and let GS = Gal(KS/K). In the case K = Q , p = 2, S a set of two odd primes, we find a presentation of GS given certain …
-
Problems involving relative integral bases for quartic number fields
… of whether or not a relative extension of number fields has a relative integral basis is considered. In Chapters 2 and 3 we use a criteria of Mann to determine when a cyclic quartic field or a pure quartic field has an integral basis over its quadratic subfield. In the final chapter we …
-
Number Fields Which Are Ramified Only at One Small Prime
The only parts that depend on GRH are: (1) In the first result when a nonsolvable image of rho does not the embed in GL2( F7 ); (2) In the second result for p = 5 with wild ramification. I plan to remove the GRH hypothesis in this part by another computer search shortly.
-
Corresponding Residue Systems in Normal Extensions of Algebraic Number Fields
Made available in DSpace on 2014-12-09T22:17:51Z (GMT). No. of bitstreams: 1 6910859.pdf: 1632495 bytes, checksum: 58e4905c38f8e7266cc90c48251903e6 (MD5) Previous issue date: 1968
-
Steinitz Classes of Tamely Ramified Galois Extensions of Algebraic Number Fields
Made available in DSpace on 2014-12-14T13:09:25Z (GMT). No. of bitstreams: 1 7524298.pdf: 2283013 bytes, checksum: b0bc8b212285c2c3858433769a9d05ca (MD5) Previous issue date: 1975
-
The Least Prime Number That Splits Completely In S3-Sextic Number Fields
<p>In number theory, an integer n is quadratic residue modulo an odd prime p if n is congruent to a perfect square modulo p. Otherwise, n is is called a quadratic nonresidue. Bounding the least prime quadratic residue and the least quadratic nonresidue are two very classical problems in number …
-
Trace Problems in Algebraic Number Fields and Applications to Characters of Finite Groups
… chapter, we define the Siegel norm of algebraic numbers, and study it in connection to the spectral norm. In the last section of the chapter we compute its values on a large class of elements of Q ≃ , the completion of Q&d1; with respect to the spectral norm. The third chapter concerns Kedlaya's …
-
Steinitz Classes of Tamely Ramified Nonabelian Extensions of Algebraic Number Fields of Degree P(3)
Let L/k be a finite extension of algebraic number fields of degree n with rings of integers ${\cal D}\sb{L}$ and ${\cal D}\sb{k}$. As an ${\cal D}\sb{k}$-module ${\cal D}\sb{L}$ is finitely generated and torsion free and thus can be written as a direct sum of $n - 1$ copies of ${\cal D}\sb{k}$ and …
-
Improved Arithmetic in the Ideal Class Group of Imaginary Quadratic Number Fields with an Application to Integer Factoring
… in the ideal class group of imaginary quadratic number fields for the Intel x64 architecture. This is useful in tabulating the class number and class group structure, but also as an application to a novel integer factoring algorithm called “SuperSPAR”. SuperSPAR builds upon SPAR using an idea …
Page 1 of 3